If the mastic is still pliable, the suggestion regarding the wire is very similar to the method used for automobile glazing repair, there is a tool with a knife that cuts the glazing gasket and I believe there are tools that use wire.
Stan, if you will be handling plate glass, do yourself a favor and get some kind of hand pump glass suction cups, you need a pair at minimum, for this job I would use 3 because its tall and narrow. Apply them to the plate glass, then work on breaking the adhesive bond, you will need a second person to hold the plate glass mirror and secure it. Use care not to flex the glass, this is a narrow piece, so carefully work your way down with the wire.
I don't know if wedging is a good idea, but it sounds like one to help provide some space to work. Remember, glass can react and break, and its unpredictable when stressed. You do NOT want to unexpectedly break this glass while working on it. I'm not sure what thickness plate you have here, but given the extremely sharp nature and un-predicability of this material, I will suggest from years of architectural glazing installation, repair and mock up testing in labs, there is always a method and a special tool to safely handle glass, its that simple.
CR Laurence is probably a high end supplier for both Auto and Architectural glazing needs, tools, supplies etc. I just post it for an example of the glass suction cups, maybe you can find these cups less costly, speak with your local glazing shop for some tips, safely remove the glass mirrors and re-sell to offset the costs of said tools to remove.
One thing I learned from supervising glazing crews, when removing existing intact or damaged glazing, experienced hands are best employed for many reasons. I would often get a repair call from a project manager on a building construction project regarding broken glass, our work usually, damaged by their laborers or other trades. Every job was unique, just like glass, and I used my most experienced people to get the job done safely, it really stood out, their experience and knowledge, on how to handle each job. I often reflect on larger and less applicable commercial work I've done to relate to small work, this is un-tempered plate glass mirror, when it breaks its dangerous, both airborne particles, and large pieces, use lots of care when handling this.
If you are going to keep the glass for future reference, make a wooden crate of sheet goods and 2x4's, pack carefully, and do not let it get wet, or allow water between to get in between the plates, you could separate them, but that puts point loading on the glass, there may be adhesive soft blocking or packing materials for this, or just stack them tight together, put a piece of foam insulation board over the last one, then close the crate. Loose plate always gets broken, and is always dangerous when it does.
CR Laurence