We can't guarantee that you will be able to save the fixtures if they are made of plastic, but we can pretty much assure you that acetone will soften the adhesive without damaging your mirror. And, although the acetone will dissolve the paint and a bit of the drywall, it will do less damage than trying to uproot the fixture without a solvent.

Use small amounts of the chemical. Superfluous flooding will not soften the adhesive any faster, and it may do damage to surrounding finishes.

CAUTION: Acetone is extremely dangerous. Read the safety instructions on the can and follow them carefully. Skin contact is not recommended, and the vapors are murder.