I reccommend the use of a product called Goo Gone... it is inexpensive and available at any home hardware store or Walmart. I have used it in the past to remove ashesive off a variety of surfacs and it should not do any damage to the mirror. You'll find it's a great product to have around.
I use a product called "Goo-gone" to take sticky stuff off of just about any surface. If you can't find it in your area, ask at your local hardware store.
Hairspray will remove it. Just saturate the adhesive, and then scrub it with a rough cloth. Repeat until the adhesive comes loose, then was the hairspray off the mirror with glass cleaner.