A liquid form of superglue applied very carefully using a needle with a tinyl drop on each corner of the frame. use a pair of tweezers to place the mirror into the frame and wear surgical gloves to lightly press the edges to seat the mirror.
Anything thicker than liquid glue may shift your mirror out of alignment and upset the focussing. Not by much but not right.
I did the same to a Minolta SRT101b years ago and it still is in place today.
There are a-cyanoacrlyate adhesives ('superglue") that allow a longer working time, look in hobby shops. The only way to damage the mirror is by mishandling, surgical or cotton gloves is very good advice. Use a Q-tip to press (GENTLY!!) on the mirror if you cannot get gloves.