Hi J, last time I had to remove a big mirror that was totally attached to the wall I first covered it in tape. After that I carefully pried it slowly and gently all the way down one side with as many things I could find that would slip beneath it. It still broke but the tape held it together so it wasn't so dangerous.
Hi J, we've done it, but it's always broken. We taped it before to minimize the shattering as the previous commenter suggested. Here's an article that may help with other ideas. Good luck! https://www.bobvila.com/articles/how-to-remove-a-wall-mirror/
Perhaps these links will help you as well! Good luck.
My son works as a builder and I get lots of mirror offcuts because they get put up wrong and get broken when they try and take them down again. They put theirs up with adhesive that is all over the back so will be hard to remove without breaking it.
Without seeing it, I would probably build/buy shelving units/cabinets that would cover both sides with a shelf over the top. If you try to remove, it will most likely break and you will have trouble removing the glue without damaging the wall. Be ready to install new drywall.