some interesting ideas thrown up there

I've tried most and can say for sure that drilling, chiselling and trying to snap along a groove all leave you with more than one piece of stone, but not necessarily straight or regular pieces
angle grinder with a diamond coated blade (for tiles and masonry) works very well but a wet running tile saw is much better

The only trouble is that the tile saws only cut to a depth of about 20mm, the stones are about 25mm