Thanks for your question! While I have not done this myself, I can’t think of a reason this should not be possible.
Generally the reverse side of this sort of acrylic is a mid to dark grey, which can be removed by the laser, leaving contrasting areas in the otherwise mirror surface (when viewed from the front).
I would advise against attempting to engrave the mirror side, as this will reflect the beam and potentially damage the laser diode / optics, but the grey side, with a flipped image, should be fine.
You may also need to paint or put some coloured card behind the mirror to aid with the contrast, though again - I haven’t tried this myself - If anyone has with mirror acrylic, please share!
There is this great post from Robert, who I believe was using actual glass mirror, with amazing results: https://darklylabs.zendesk.com/hc/en-us/community/posts/360007540795-The-Core-so-far
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