The mirror glass part can be removed fairly easily but you must be careful. Two weeks ago, my wife came home and said she needed to show me something with the truck's passenger mirror. The mirror glass had gotten loose and was just hanging by the electrical wires. I don't know how it happened. The bottom of the mirror has two tabs that fit into small openings on the bottom of the the electric mechanism that turns it, the top has two snaps with little tabs that snap into to openings on the mechanism, the defroster is a heating wire connected to two wires coming from inside the door. I centered the moving mechanism, put the mirror's bottom tabs in at the bottom of the moving mechanism, aligned that upper snaps with the openings and pushed till I heard a snap.
I think if you wanted to remove the old glass, use two pieces of wood like paint stirrers and insert them at the top of the Glass about 1 inch from the corners and gently force the snaps to pop out. Reverse the process for installation. I think once you remove the glass you can test it and make sure it's the heating wire before replacing it.