This is the method I use, either to harvest wool for spinning, or just to remove the wool for the sake of good grooming, health, and hygiene. Some of this applies to show Angoras, some doesn't. I clip my Angoras about every 3 1/2 months. At that time, the wool is long enough for good spinning, but it's a short enough period of time that there is very little matting, even with very minimal grooming between clippings.
These are my grooming tools. I use the red slicker brush for a quick brush-through before and after clipping. Most of the clipping is done with the small, orange-handled Fiscar scissors. I only use the larger Fiscar barber shears a few places and for evening up the length of wool when I'm finished. Many people like the gray-handled Fiscars, but I prefer the others. Wool clipping time is also nail clipping time. My nail clippers are on the left. The other red-handled device is for clipping overgrown teeth, if that should ever happen. I don't use the comb very much, but it is helpful for small mats, especially on the ears, cheeks, bangs, and feet. And last, a lint brush to clean my apron and clothes when I'm finished.
Any small to medium, sharp-pointed scissors will do. They do need to have sharp points and a thin blade to easily slide through the wool. I have electric clippers, but I don't use them. The blades have to be super sharp to cut the fine English Angora wool. Also, I don't like the noise, and I get second cuts in the wool, which all spinners hate.
Clipping or grooming can be done either by setting the rabbit on a small table, or on your lap, or alternating with both; whichever works best for you. I used to use a table, now I use my lap.
If you're going to be saving wool for spinning, first give the rabbit a quick brushing with a slicker brush. This isn't to remove mats at this point. It's too late for that. This brushing is to remove bits of hay, fluff out strands that are made by the rabbit licking itself, and brush out little noils that are sometimes on the surface of the wool. This isn't a thorough brushing. A thorough brushing should have been done several times, or at least once, during the wool-growing period. Also, if you're going to be saving the wool for spinning, set up three bags for sorting the wool as you go. I use plastic grocery bags, and these work perfectly for me for storing the wool too. In one bag, I put the top quality, clean, mat-free (but a little webbing is OK with me) wool that is at least 3 inches long. In another bag, I put wool that is dirty, matted, tightly webbed, and short. This gets thrown away. In the third bag, I put wool that is in-between. It is spinnable, but lesser quality. This wool is clean, but can have small mats, a fair amount of webbing, shorter than 3 inches, but long enough to spin. This is often belly wool; sometimes even wool from feet, legs, bangs, ears, etc. This wool is good for blending with other types of fibers, such as sheep wool.
Part the wool down the middle of the back so you can see the skin. Use the fingers on your left hand (if you're right handed) to hold the wool back and slightly taught. Start cutting at the part, making small cuts, in rows, going down one side. Clip very close to the skin. Run the bottom edge of one blade right along the skin. That way, you will be able to see the skin as you go, and are less likely to cut the skin than if you were cutting the wool longer. Also, with the bottom edge of the blade along the skin, you know the skin is not in the cutting area. You can make several cuts, then grab the cut wool with your left hand and place it in the appropriate sorting bag.
Turn the rabbit around, and do the same with the other side. The back end can be done separately, or with the sides, however seems best. Work forward on the shoulders and neck area as far as you can reach. After you have clipped a few rows from the center of the back, it really doesn't matter what order you clip in. If the rabbit wants to turn around, you can start on the other side. Just don't let the rabbit move too freely, or often, or this process will take a lot longer than needed. I usually clip awhile on the top-side of the rabbit, then turn it over and clip awhile on the underneath side. This alternating gives both the rabbit and myself a change in position.
This is my chocolate tort doe, Jo with most of her wool cut off. You can see how short and even her wool is on her body. I've cut her bangs, but not the wool on her ears. I still need to cut the wool on her shoulders, front feet and legs, and chest. Jo is sitting on an apron on my lap. Notice the scissors I have been using and the three bags of wool that I am using to sort the wool in as I go.
For the underneath side, I recommend sitting down, with the Angora on your lap, facing you. Have on a large heavy apron, or put a thick towel on your lap. Take your left hand, grab the rabbit's shoulder skin, near the neck, with its ears under your hand. Your hand will be coming at the rabbit from its back. That is, when you are grabbing the skin, your thumb will be on the right side of its body (near the left side of your body). Use your right hand to cradle the rabbit's behind, and roll it over, up-side-down. Rabbits sometimes tense up at this point and kick. If this happens, while your right hand is still on the rabbit's rump, your right thumb is sticking out, close to the rabbit's belly. Put your right thumb on the rabbit's belly, with a little pressure, and stroke downward, toward the back legs. This almost always stretches and relaxes the rabbit. Slightly move your legs apart. Put the rabbit's shoulder area between your knees. The apron or towel will be like a hammock, and your legs will gently press against its sides. The rabbit's head should be slightly lower than its back legs. Most Angoras don't mind this position at all, and get very relaxed. Laying on their back is not an unnatural position for a rabbit. They will jump up sometime though - some a lot, and some very little, so be prepared to catch the rabbit, so it doesn't fall on the floor. If the Angora has been on it's back for some time, then jumps up, it probably needs a break from that position, so you can work on the top side of the body for awhile. If the Angora is wanting to jump up often, like every minute or two, put it right back down, so it will learn that it really does need to lie this way, and should relax.
This is Jo, lying on her back, on my lap, partially clipped. She is calm and relaxed. In this position, you can clip all the wool from the legs, tail area, belly, chest, under chin, etc. I start with the bottoms of the back feet. Clip and brush out all the mats, even the little ones between the toes. Be sure not to clip the wool too short on the bottoms of the feet, because the rabbit needs a cushion to prevent sore hocks. After I've done the bottoms of the back feet, I start at the top of the toes, clipping very short, work my way down the legs, around the tail area, and the tail itself. At the base of the tail, I clip the wool very short. But I leave a tuft of wool on the end of the tail, starting about half way down the tail. Be sure to watch for testicles on bucks. Just like with other body areas, if you cut the wool very short, you can see the skin with each cut, and aren't likely to cut anything hiding in longer cut wool. I continue clipping down the belly to the front legs. Then I clip the front feet the same way as the back, down the front legs, and continue with the chest and under the chin. Some rabbits are very ticklish on the chest, where the front legs join the body. It can take some patience to clip this area.
With the rabbit in the up-side-down position, it's a good time to clip the toenails and check and clean the scent glands. For nails, use clippers designed for cats or dogs. On a white rabbit, you can easily see the blood vein. On a light colored rabbit, you can probably see it, unless the nails are very dark. With dark nails, you may have to guess. Leave just a little nail beyond the blood vein. I usually take 2 or 3 clips to get to that point, just a little at a time. Rabbits have 5 nails on the front feet, and 4 on the back. Don't miss the "thumb" (dew claw) on the front feet.
Rabbits have a scent gland on each side of the vent area. It's in a little pocket that's usually closed and can be hard to find unless you know where to look. This pocket can get a build-up of a dark waxy substance. It smells really bad, so it's a good idea to use a cotton swab, paper towel, or something so you don't have to touch it with your fingers. The pocket will have it formed into kind of a sunflower seed kind of shape, so it's really easy to pick it out. It's not necessary to the rabbit's health to clean this out - just kind of a good grooming thing to do. And you don't have to clean the pocket well - just take out the waxy piece. Rabbits also have a scent gland under the chin. Rabbits rub their chin on things to leave their scent. This is called "chinning". You may, or may not, be able to see a spot under the chin that looks slightly wet and matted. Sometimes the hair will be in a swirl. Brush out, and trim off the wool in this area.
I usually don't clip the ear furnishings. I just comb them out. You can clip them short if you want, or clip them down half way. In hot weather, I do clip them short sometimes, to help the rabbit's natural cooling system of air moving over the blood vessels in the ears. If the furnishings are matted, you may have to clip at least some of them. I usually clip the bangs and cheeks short, but if you want to leave about 1/2 inch bangs for cuteness sake, that's OK too. Mats can hide in the cheek furnishings, so be sure to get that area completely clipped, combed, or brushed out.
All finished? Give the rabbit an all-over brushing. Even when the wool is cut very short, there can be the beginnings of little webbings at skin level that can grow into mats. Check for any mats you may have left between the toes, under the front legs, between and behind the ears, cheeks, etc. Little mats now, will be big mats later. But most important, that last brushing will remove tiny bits of wool that you don't want your Angora to eat when it licks itself. Finally, if you want, use the barber shears to even up any longer or uneven areas. Now you're really finished. Put the Angora back into its cage, where it will lick itself all over. It will be so glad to be free of the wool and have unobstructed vision, it will jump around and have a good time. Give it a treat, just to reinforce the good of the experience.
Rabbits and people both get tired, so you may not be able to clip your Angora all over at one sitting. Clip until one of you gets tired, then both rest for awhile, or even a day. Make the Angora understand that this is serious business, not play time, and the rabbit can't run away from it, or act nasty and you will let it alone. Let the rabbit move a little bit to change position and get more comfortable, but not to the point that clipping is hard for you, or that the rabbit thinks it is boss. No, really, YOU have to be the boss, for the good of the rabbit. A complete clip of an English Angora takes me about two hours. I know, I'm slow. Most people don't take that long. But I do a careful job, hardly ever nick the rabbit's skin (I've cut my own finger more times), and I have excellent quality spinning wool in the end.
I believe that every Angora owner should be able to care for their rabbit, and care includes removing the wool periodically, either by plucking or clipping. Yes, it is a chore, but a very necessary one.