Maybe by exploiting different solubility in water.

Or by crystallization with gypsum as seed.

https://www.google.com/search?q=naica&tbm=isch

Another idea would be to do electrolysis with

copper electrodes. The copper goes into solution,

and copper sulphate crystals should be easy

to grow.

Regards,

Joachim

Density calcium carbonate is 2.71 g / ml, and calcium sulfate is 2.32 . Try to separate them in heavy solvent - methylene bromide, its density is 2.49. Pops calcium sulfate, calcium carbonate will remain at the bottom.

Try bubbling Oxygen gas through the suspension.  The Calcium Sulphate (gypsum) will precipitate.