I have used heavy braided nylon masonary string to remove mirrors installed in this fashion. Place the string behind the mirror and used work it back and forth to saw through the adhesive. This method will not damage the drywall or the silvering on the back of the mirror. This method only works if you have sufficient space on either side of the mirror to work and not if it is butted up agaist a side wall or a cabinet. I have also used this method to cut PVC pipes in tight spots where a saw can't reach.