Once you figure it out, PLEASE post what you did to gain access, and if you also had to cut an access hole in the wall behind the mirror. As these coaches age, many of us are going to have this problem.
Pictures would be very helpful after the mirror is removed.
One idea mentioned above is use fishing line to cut the tape or caulk behind the mirror. Not an easy task but it should work. Or you could use piano wire.
2001 Monaco Diplomat 40' PDQ - 08 Honda CR-V