Use your knife to cut the rabbits hide on the middle of its back. Cut towards the top of the body, making an opening within the hide. Hold the head of the rabbit with one hand. Use your other hand to reach inside the cut and grab the hide. Pull that hide back towards the tail of the rabbit. This will be surprisingly easy, as the hide is barely attached to the rabbit and will slide easily. Pull the hide all the way off, over the hind legs. Try to peel off as much of the remaining fur as possible, or at least get all the major pieces.
Grab the tail and give it one good yank to remove. Now you should grab the rabbit with one hand by the hind legs. Use your free hand to pull the remaining hide from the front of the rabbit. Pull it far as you can to the head. Pull that hide over the front legs until it is no longer attached to those legs. Now remove the head. At this point, the hide should be pulled over the head, but still be attached. Place your knife at the base of the neck and cut off the head. If you’ve done everything correctly, this will remove the head and remaining fur in one step.
There will still be hair on the bottom half of both legs. That doesn’t matter because there’s no good meat in that section to be eaten. Break the section of each leg where you find a joint. Cut off the bottom half of each leg at that spot. Now you will clean out the guts. Make a cut in the ribs and work toward the tail. Don’t cut too deep, as not to puncture internal organs.
You are really just cutting the skin in a straight line down the rabbit. At the same time, separate the skin to each side. At the bottom of the pelvic section, you will need to pause to pull the guts up toward the middle of the rabbit. This will keep them out of the way as you cutting. Now finish cutting the pelvic bone, separating the legs. Reach inside the chest and grab the heart and organs. Work them down through the middle of the rabbit and pull them out the bottom. The organs will stay together if you have a good grip.
Look for any remaining large pieces of fat or skin and pull them off as best you can. You now should have nothing left behind but the cleaned out body.
You now have the option of leaving the rabbit as is for cooking, or cutting it up further. If you choose the latter, cut the rabbit into five smaller pieces by separating the legs individually. Also cut the rib cage off, leaving the bottom section of the rabbit. The rib cage has no meat and can be discarded. When you are done cutting, you can clean the body off with water. Rinse off any blood, fur, and dirt and you are ready to cook.