Hi. Typically the mirrors are not glued all over the mirror. It's usually down the sides and in the middle. Take a putty knife and try to loosen the mirror. Be sure and wear protective clothing and eye wear. Cover the sink and floor with plastic or a tarp. You're probably going to need an extra pair of hands to assist. You may get lucky and the mirror pops right off - whole. But it may also break. Broken mirror makes great mosaic pieces! Good luck!
Perhaps these links will help you as well! Good luck.
Take the clips off, cover everything in the bathroom, wear rubber gloves and eye protection. Take a putty knife and run it along the sides. If it does not pop off tape off the mirror and hit it with a rubber mallet.