Is there any way to change the glass in an interior mirror?

[Clemson88]

I have/had two one of which had a perfect mirror and the other a nice functioning frame. I pried on the plastic cover over the good glass and it chipped without separating. There was residue of some type mastic which held the body and that retaining cover together.

I tried prying on the good body to change the mirror but it resisted. Is there perhaps a solvent which would break the glue bond without damaging the plastic frame?