Never let your puffer puff up...especially with air. It can be very dangerous for your puffer.
You can use clove oil to anesthetize the fish and they cut the teeth with nail clippers or use a file to shave them down. Google "clove oil puffer" or "clove oil fish" and it should pop up with a bunch of good info. There are specific products for anesthetizing fish in the fish trade but they are usually costly and clove oil works just as good and is pretty gentle. After you're done, plop the puffer back into fresh saltwater and it'll revive shortly. Good luck...