Rough cut the pieces with an angle grinder. Mark the piece of slate on the back side where you need the piece cut. Hold the grinder in both hands, turn it on, and score the back of the piece roughly 1/8 inch into the stone on the back side. Hold the piece firmly in your hands and snap the waste edge of the piece against the ground, forcing the tile to break along the scored line. This will give you a ragged cut.
Hammer and chisel the cut to create a rough-hewn look. Mark the tile on the top side where you want to cut it, and score the top edge of the piece of slate along the mark with a hammer and chisel. Snap it against the ground as you would with a back-cut piece to break it off, or chisel the edge off if you have a smaller cut that cannot be snapped.
Break the slate up into smaller pieces for natural break points if you prefer the roughest edges. Wrap the slate in an old towel and use a rubber mallet to firmly hit the piece. While the results will be somewhat unpredictable, you can control the break points to some degree by smacking the piece with the mallet along an edge near where you want the piece to break off.