He might be biting his tail out of stress or boredom. Also, some fish with very large tails will bite them so that they can swim easier.
If it's boredom, it's pretty easy to fix the problem by adding new decorations or plants to his tank, or moving around what he already has. I put hamster tunnels in my tanks, and the fish love them. If it's stress, you need to find what the problem is. The water might be too cold or not cleaned often enough, or maybe the tank is too small.
The actual damage isn't a big problem. If you put a little bit of AQ salt in the water, that'll help prevent infection, but it should heal quickly without treatment once you get him to stop biting.
My BettasDavros, multi-colored veiltail maleSpock, blue veiltail maleOswin, red veiltail femaleCastiel, blue and white Delta maleGandalf, marbled veiltail maleDr.Horrible, yellow veiltail male