Spectra (high strength polyethylene) is strong in tensile strength, but has a VERY low melting point. If you saw with it, it will probably break.
I would consider using Kevlar* cord. You can get Kevlar braided line as used for kite lines. It will work better as a saw than twisted lines.
In fact, it works so well as a saw that it is considered too dangerous to use when flying near other people. Don't try to hold it with your bare hands; use sticks or rings to hold the ends. Don't leave it attached to anything where someone could get caught in a loop and cut themselves. It will go right to the bone.
If you have to knot it, sleeve it with hollow braided polyester (Dacron) line before tying. A long narrow loop of fine music wire will push through the hollow-braid polyester to pull the Kevlar through. Visit a kite shop, and you will find sleeving needles (the wire loop), Kevlar cord, and polyester sleeving material.
Cruder but easier: cut a couple 3/4 x 3/4 sticks and wrap the cord around one several times and clamp or screw the other tightly to it to make a handle.
(*Kevlar is a trademark of DuPont. They write me to complain every time I fail to mention that.)
Braided Wire, Hit a glass shop and ask them for some of the braided wire they use to remove auto glass. It will cut through the tape like a hot knife. Or use a heat gun to melt the adhesive. But that could also damage the mirror. If the aluminum isn't that that thick you might try a good auto body suction cup and pull it back.
3M has a PDF document on removal. Did a search for "3M VHB tape" and got it directly from 3M's site. It's all mechanical systems to air hammer a skinny chisel in between the parts and a buffing wheel to remove the residue, though.
I recall having to disassemble things like this before, and it was a royal pain. Started with a bunch (a bunch!) of thin wedges and a heat gun. Starting at one corner and working your way carefully to minimize preload on the glass, slip the wedges in as the adhesive warms up and softens. You might be able to take advantage of the preload already in the glass, but there'll be a point where it pops and the glass could break. Maybe putting shot bags on the glass would help. The tape won't be all over the place, just applied in strips, so trying to keep the wedges where the adhesive isn't will keep them from gumming up with adhesive.