Step 1:
To prevent the mirror from cracking or shattering, cover it with heavy-duty tape. Tape it in a crisscrossed or checkerboard fashion.
Consider placing something over the sink, vents, and toilet cover, in case it does break. You should also wear thick gloves, and eye protection.
Step 2:
Place wooden shims in any spaces you can find in between the wall and mirror. You can buy shims at a hardware store.
Step 3:
There are a couple of ways to remove the mirror. You can use just the shims by tapping them further behind the mirror, which should loosen and unglue it.
Or you can use a pry bar. To do this place another wooden shim on top of your mirror, and place the pry bar against it. This way you can apply more pressure without damaging the wall.
For both techniques make sure you apply steady pressure, and work your way from the top of the mirror, to the sides of the mirror, until you reach the bottom. You want to try and unglue a little bit of the mirror at a time, so it does not unexpectedly fall.
Step 4:
Once you reach the bottom of the mirror, make sure you are still supporting the top of it. If you do not support the top of the mirror it could fall, which could cause serious injury.
You can also try wiggling the mirror to loosen the bottom.
If you do not think you can support the mirror while ungluing it from the wall, ask someone to help.
Step 5:
Once it is loose, gently lift the mirror and carry it out of the room. If you plan on using the mirror again, make sure to wrap it up, and put it where it will not be damaged.