I use a big Hobbart. I cleaver the carcass in half, length-ways, and put the whole thing in.
You have to make sure your blade is sharp, and the the end float is controlled to ensure a good tolerance between the blade and the anvil.
When work allows I.e. time... I mince 30-40 headshot rabbits up, and freeze in portion packs.. just need to slip the jackets off, and drop the guts out. bone and all, it is all my dogs favorite food.