Any GF water-based finish can be removed from a mirror using 0000 steel wool and Windex.

Wet the steel wool with Windex and buff the glass. (The steel wool won't harm the mirror but make sure that you don't apply so much liquid that it seeps into the backing.) Wipe the mirror down with a clean/dry paper towel.

However, you can prevent a mistake from happening by applying Frisket to your mirror BEFORE applying finish to the frame. Frisket is a clear finish that brushes on, dries and peels off when you are done painting.

*Windex Warning: Make sure you do not get Windex on water-based finishes. The ammonia in Windex may cause a cloudy appearance to the finish.