I use a scrollsaw and it works like a charm. No chipping etc. After I cut I use a mechanical sander to smooth and neaten the edges. There's no reason you can't hand sand the edges either, but I'd suggest laying the paper on the table, face up, and run the board edge along the sandpaper surface....makes for a neat, straight edge.
These cut edges are extremely porous so be sure to seal them well. (you will have to black them also, to cover the raw mason board.)
A hand fine saw would work well also. The small 'D' shaped jewellers or craft piercing saw. It will be essential for the teeth to point DOWN when sawing or you will be likely pull the ink/clay away from the surface.
I hope this helps.