You can break the mirror, but please do remember that these mirrors are here for a reason when they're not possessed and breaking mirrors is decidedly very, very bad luck. Your character may find themselves cursed with bad luck, to see themselves on their death bed in every mirror they look into, or generate grudge spirits out of any future mirrors (think like, Sadako except crawling out of mirrors in the dead of night). Dealer's choice. It's a deep curse, so you may need more than one siphoner to work together to remove it.

..And of course, the reflection will just appear in another mirror. It is just a reflection, after all.