Even if you cut it clean; open edged squares will create a lot of dust during handling.
May I ask what specifically this is for? Perhaps there is a similar, easier-to-handle choice of material.
That being said, if you must do this, I would use a straight edge, score. Snap away from the score, then score the other side which will present a crease.
The rough gypsum edges can be run against a block, clamped to the bench that has been faced with 150 grit sandpaper.