Fin nipping can kill over time because the fish will become stressed. It is generally accpeted now that fish do feel pain, though it is still debated, so I would say that yes, it is hurting them.
Do fish fins grow back after nipping?
Yes, the fins of a fish can grow back after nipping or rot.
Fin rot can also be caused by a secondary infection on a nipped fin. From experience, your fish will recover, and the fin readily grow back in pristine water with the appropriate quality for the species you are keeping.
What to do when a fish is nipping?
What to Do for Fin Nipping Fish
- Removing the Fin-nipper. Remove the offender immediately before it does further damage to the rest of its tank mates. ...
- Rehoming the Offending Fish. House the fin nipper in a separate tank or find a new owner if you are unable to give it a tank of its own. ...
- Treating the Victims. ...
- Prevention.
