Yes you can trim their claws and yes they do grow back again. You just have to be careful that you don't cut them too short. When you expose the claw you will see a vein inside the claw just don't cut them short enough that you clip that vein. It's not a major catastrophe if you do, I know I have accidently done it, but it is painful for the cat. If it's the first time, your cat will probably do a lot of squirming around and crying but he will get used to. Mine still don't like having it done but they are good about at least tolerating it.