Haven't tried it myself, but there is a scan of a technical manual showing the removal process here:
https://www.planet-9.com/threads/internal-rear-view-mirror.238071/Scroll down a few posts in the replies and there is a PDF. They show a locking pliers with non-marring jaws, you might be able to duplicate by wrapping the mirror base in cloth.
Or wait for someone who's done it to chime in.