They are in a tank that is too small and behaving territorial as a result of being cramped up. If they are hurting eachother as you described, you need to separate them IMMEDIATELY. Missing chunks of flesh is a huge red flag.

If I were you, I would upgrade my tank to something much larger. The rule of thumb when dealing with turtle tanks is 10 gallons of H2O per 1 sq. in. of turtle. It sounds like your turtles are much bigger than five inches, and if you keep them together it will only get worse.

Good luck!