How to Remove Scratches from Glass
Could be held on with concealed mirror fasteners (usually a clip or notched "button" design, with very litle showing outside the mirror, or none showing if has trim around it, or with large dabs or swipes of mirror adhesive or liquid nails. The former leaves minimal damage when removed - no more than a heavy duty picture hanger, the latter leaves divots in drywall, as you surmised, and holes in the drywall if a piece of plywood is not used as a prypoint when prying it off.
If you want to try to save the mirrors, then a glass and mirror installer is needed - they can remove them from the hangers, or cut the adhesive with wire saw - though that will add probably 2-3 hours labor per room. Then you would need a painter who also does minor drywall repairs.
If not saving the mirrors, then I suspect you could get a Handyman to pop them off, repair the divots, and repaint. Otherwise, a Painter would probably be glad to do it and repair the damage and repaint - just be prepared for a hefty charge for duct tape - like $100-200, because that is the best way to do this - duct tape the surface completely, pry the mirrors off (commonly breaking them), then cut through the tape to make pieces of glass manageable and of a size to fit in garbage can or box for hauling out. Be sure to emphasize PLYWOOD protection for floors, overlain by canvas or plastic, when removing the mirrors - drop a good sized piece and you have significant flooring damage.
Here is a prior response for a similar situation, including the same suggestions about removal, but also a bunch of ideas of how to leave the mirrors and cover or integrate them - which can be a LOT cheaper than paying a two-man crew for a day to remove mirrors, depending on solution you choose.
this is probably a quarter to full days job to remove depending on how fastened and if saving or not, so about $200-800 range. Drywall repair and painting probably about another $150-250 range, so ballpark numbers - pushing $300-400 if mirrors come off easy (bracketed) or can be scrapped, more like a thousand $ if saving mirrors.