If a rabbit is bleeding BAD, try to stop the bleeding and take them to a vet. This could lead to death very quickly.
Small cuts can be bandaged, and bleeding can be stopped by using corn starch, or various other blood stopping powders on the market. If you clip the quick (vein) while cutting the toenails or fingernails, get a paper towel and wrap it around and apply pressure to stop the bleeding. Bleeding from the nails or after an ear tattoo is not life threatening.