Never mind, I thought you meant the other mirror. Maybe still try the fishing line trick to cut the adhesive?I’ve never taken that mirror off on mine, but I’ve heard from another 37 owner that the panel the mirror is bonded to is just attached to the cabinetry with Velcro, like this -
View attachment 209288
Once you have the board off it should be possible to separate it from the mirror with a putty knife, or maybe fishing line to cut the adhesive. Maybe have the new mirror ready to reinstall in case the old one cracks on the way out.