How about setting up a big, giant magnifying glass, and focusing it on the patch of gypsum we want to dewater?
Actually, RF generators set below the surface could provide a more controllable source of energy input. Heat the water at depths to steam, then as the steam rises, it will do the work of releasing the crystallized water from the mineral.
But for all this, you need some power input. Solar generators?
How do you get water from gypsum? Simple; just add water.