Unfortunately, it may not be easy to remove, and whether you try a physical or chemical method, there is a good chance of damaging the thin reflective coating. Mirrors are typically mounted using this type of adhesive, and the safest thing to do is to leave the old stuff alone and to simply remount the mirror using similar adhesive. Put the new blobs in different locations than the dried stuff, make the blobs big so that when you press the mirror to the wall you will have good adhesion, and when you're done you shouldn't have the mirror standing off from the wall any more than it was originally.

thanks for validating what I thought may be the only way. I have screwed up a mirror before trying to get this tuff off. This piece of glass is way to expensive to take a chance on.