The mirror is the Beast's only window to the outside world, the only way he has to check up on things without lynch mobs forming to kill him. (Turns out, they do that anyway, but never mind that.) That makes it a pretty clear symbol: a window to all the things he can't have and a reminder of all the things he's lost.
That symbol works against him when Gaston gets hold of it. In that instance, the window becomes a weakness: revealing him to the world and putting both him and the rest of the castle in terrible danger. In that sense, the mirror exists as an eternal tormentor, revealing his needs and desires and sending danger his way.
That also makes it a symbol of his imprisonment, which doesn't have to involve actual bars and locked doors. He's an outsider, stuck behind fear and misunderstanding. We never see the mirror again after the curse is lifted. There's a reason for that: he's not imprisoned anymore.
Belle's love has freed him, and with it, the mirror has finally lost its power to torment him.