"> How would you go about it? "
Well, let's see. It would be a good idea to know how the top was fixed
to the cabinets, the measurements and relative positions of the
components to be saved, scrapped, re-installed and so forth.
So, the first thing I would want to do before venturing any advice
would be to come and look at it closely.
If mirror glass is attached with mirror mastic, a piano wire can be
used to cut through and remove the mirror.
But, from here, I can't tell how they attached the mirror!