Betta are pretty smart fish. If you have the mirror in a fixed position, they'll generally learn to ignore it after a couple of days or so. But it depends on the individual fish's temperament. Some betta are psychotic and will flame on at just about anything that moves, all the time (which is probably not very healthy). Others are very docile and never flare. Most are somewhere in between.

I keep Nobunaga, my red/blue crowntail betta in a tank with a mirrored background, along with some red-eye tetra and corys and chinese algae eaters and he's cool as a cucumber. In fact he interacts well with the other fish, I've never had a single incident with him. Occasionally he'll flare up when the algae eaters go chasing each other around the tank at ramming speed (which they love to do), but he's never attacked them. A lot really depends on how aggressive your specific fish is.

Bottom line, it's normal for betta to show off once in awhile, but if they are doing it constantly and on a daily basis you should probably remove the offending item.