If you're really stuck you could:
Use a bench or band saw to VERY carefully remove the wood through shaving the back off while holding the mirror upright. Then remove the glue with a chisel or scraper or razor. This could be dangerous if the saw binds in the wood and draws the mirror and/or your hands into the blade. Perhaps make a jig to hold the mirror vertical as it works against the saw.
Use the same jig with a hand saw instead to remove the wood. Much safer but the jig will need to be substantial to withstand the sawing.
Make a wooden jig to hold the mirror horizontal and use an electric plane or manual plane to shave the backing down to the glue/silicon. Then remove the glue with a chisel or scraper or razor.
Firmly fix the mirror and chisel the ply or wood away by hand.
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