Why does my cat shuffle his backside across the floor?

Your cat may be trying to clean its bottom. Try washing it for him with a soft paper towel or tissue with just plain water. He might be constipated, but you would have to observe his going to the bathroom to be able to tell. If so, a little bid of mineral oil in his water or milk would care that problem. The worst scenario is that he might have worms. You can see them if he does. He would need to see a vet to get rid of them.