I have recently changed some mirrors at home that were stuck on using double sided adhesive tape, I say at home because now I do not have a boat, but the method used to put the mirrors in place initially had been the same as when I replaced them on the boat I had at the time, namely a B36(2002).
What I used was a long thin and fairly fine toothed hack saw blade with some tape wrapped around one end to form a more comfortable handle than trying to grip just the blade. By keeping the handle area as thin as possible allowed the saw blade to pass easily behind the old mirror. With the blade between the mirror and the wall I was able to find the double sided tape, and to saw down through the middle of each strip of the tape, and without damaging the coating on the back of each mirror. Careful positioning of the blade allowed each strip of tape to be cut through, and the mirror came off.
Once off the remains of each piece of double sided tape on each could be peeled away easily and then washed in a suitable adhesive remover to remove the last remnants of the tape. The new larger mirror was then fastened in place using the same double sided adhesive tape.