Your signature says it is a betta with split fins, so it is probably from biting his tail or poor water quailty. Is there anything in your tnak that could be stressing him out? I've seen bettas bite their tails from a filter current, seeing other fish through the divider, seeign reflections, and being bored.
Also, is he in a cycled tank? if not, are you using something to elimnate the waste and changing his water once a week?
For rerowth, adding salt and also melafix (use half a dose) seems to help.