To add to what Dr. Humphries stated, what you have described is very typical for a dog bite injury. The extent of the trauma is often not seen for 7-10 days. Wet-to-dry bandages are typically used in treating this type of wound and, as Dr. Humphries said, removal of the bandages shouldn't pull up new skin.
The wound may or may not require debridement (removal of dead or necrotic issue). It sounds like skin flaps or grafts will be required. Again, I agree with Dr. Humphries that your veterinarian should examine this wound -- regularly -- to ensure proper healing.
Best wishes for kitty's recovery. Sounds like the little guy has had more than his fair share of trauma.
Bad small is dying (or necrotic) tissue. It is probably infected because of the ever present skin bacteria. This type of wound will take much nursing care for many months. The skin flap may also die and that necrotic skin will have a bad smell and cause a source for infection. Sounds like this wound needs a quick look by your veterinarian. You may very well be able to handle the nursing care of this wound until healed, but I would guess it needs your veterinarian's exam frequently so as not to let either necrotic tissue or infection get so severe as to be a threat to life.
I would also make sure with them you are doing this bandaging correctly. You should not be pulling up newly formed skin!