The mortar bed is going to be the hardest to budge. I had just a small amount to remove so I used a chisel and hammer. I believe there is a jackhammer type tool that holds a flat ended metal piece, I'm sorry I don't know what it is called, but it can be rented. It will help you get under the mortar as well as the slate. Be prepared, it's messy as well as tiring. And Scott is right, get some safety goggles!