Cheryl, I had the same problem 2 months ago when I wanted to put up a medicine cabinet. Heres what I did after researching. I bought this liquid stuff called "GOO GONE" found at any home depot or hardware store... I started from the top of the mirror and started pouring this liquid stuff down behind the mirror left and right back and forth to make sure the whole backside of the mirror gets it. Pour about 1/4 of the bottle then wait 10 minutes for it to set, then repeat one more time....I then used a screwdriver or crowbar and started prying the mirror off.. I couldn't believe it came off!
I had tried using the hairdryer but that didn't work... The mirror is heavy so make sure your holding it up as your prying - Also, make sure you dont crack the mirror when your prying. You will see 6 or 9 big black goo things on corners and middle which is the glue holding the mirror up...Good luck!