Hi, I've cut a few sapphires that I've found at the Willows down to as small as 2.6mm dia. the cut being a petal cut. I would guess your 4mm stones would probably cut a 3.5mm dia. stone, so the thickness needs to be about 2.5mm. However I would recommend getting some practice cutting small stones in quartz or other cheap material, as working with rough that small is not easy.