According to Lowe's, one of the best ways to remove a mirror that is glued to the wall is to cover the mirror with packing tape before gently prying it off with a pry bar. Materials for the project include gloves, wooden shims, a small pry bar, packing tape, spackling compound and primer. One additional person is needed to hold the mirror while it is pried off the wall.
Cover the mirror with heavy-duty packing tape to prevent cracking the mirror when it is pried off the wall. Insert wooden shims in the gaps between the mirror and the wall without forcing them beneath the glass. Gently pry the top of the mirror from the wall using a shim to protect the wall above the mirror. Work down the sides and then the bottom of the mirror. Use an additional pair of hands from a friend to support the top of the mirror to keep it from falling and breaking. Gently carry the mirror away. Repair the drywall surface by spreading drywall patch over it and then priming the surface before painting.
Other ways to remove a mirror are by using a piano wire to saw it away from the wall or by using a special suction device. This Old House explains that options are limited because the mirror can break at any time during the process. Professional glass companies have specialized equipment to minimize broken glass during a mirror removal.