What to do if your cat damages a nail:
Initially, you will have to stop the bleeding. You can use silver nitrate or styptic pencils. If you don't have either of these, try cornstarch or flour. When placed on a bleeding nail, these generally stop the bleeding.
Removing the loose nail is the most difficult part of caring for the torn nail. Most often, you can just pull the loose piece of nail off very quickly. If the nail doesn't come off easily, you can try to use a pet nail trimmer and remove the nail at the level of the break. Remember, this will probably hurt your cat for a second. If the tear in the nail is high up and near the base of the nail, don't attempt to remove it with trimmers. If the nail isn't easily pulled off, see your veterinarian for treatment. The last bone of each toe is very close to the beginning of the nail. Without experience, you may end up hurting your cat more than you realize.
If you manage to remove the damaged part of the nail, gently wash the area with warm water to remove any debris lodged between the nail and the toe or leg. Then apply a temporary bandage if necessary for bleeding. Take care not to wrap the bandage too tight so circulation will not be damaged. Leave it in place for 12 to 24 hours.
If you do not feel comfortable taking care of a torn nail, call your veterinarian. Leaving a torn nail to heal on its own (which will not happen) or allowing the nail to grow out is not a recommended option. This causes persistent irritation and possible repeat breaks.