How do I remove peel & stick tile installed over asbestos tile?

You should be able to remove these without damaging the face of the Asbestos tile too much.  I would recommend an adhesive remover.  Let this product soak in and dissolve the glue instead of digging into the tile that is beneath.  Asbestos is not a risk until it is torn-up and in the air.  If you were to install a new floor over this you would be encapsulating the Asbestos which is generally acceptable.