Fishing line or stainless picture frame hanging wire.
Get the fishing line or wire between the back of the mirror and the wall and drag it through the double sided tape with kind of "seesawing" through motion.
You DO want to take some duct tape or packaging tape and place it on the broken mirror in a criss cross pattern and depending on how big up and down and straight across..
The tape will hold any big pieces that break in the process.
Wear some good leather gloves, eye protection..
Barring that try a heat gun (ELECTRIC, DO NOT USE A FLAME THROWING TORCH) to help soften the adhesive (but don't over heat the area, it can set the wall on fire if not careful).