While it is true most betta fish have their fins torn, being so long and impractically decorative its hard no to, they will not grow back. Usually it does not hinder the fish’s ability to swim, but if you’ve taken an entire pectoral fin off it might make it a little more difficult, tho I doubt it would make too much a difference.
She should still be able to rise to the top to feed/breath. Betta fish have a labyrinth organ that makes it possible and necessary to breath in oxygen so its essential they always have access to the top of their tanks. If she can not get to the top, she will die of suffocation.
However, since they dont really use their pectoral fins for anything other than steering, your fish will probably be just fine.
From - http://www.freebettafish.info/will-b...ins-grow-back/