Natural stone such as slate, granite, limestone, sandstone, and other materials, are some of the hardest floors to remove. Unfortunately there is no way around it, the process involves a considerable amount time and manual labor if you want to do it right.
The first thing you should do is remove and base moldings that you may have. This can be done using a crowbar, propped against a piece of wood. The wood is butted against the wall, to protect your drywall from damage.
Once you have removed the molding you should inspect the floor to see if you already have any loose tiles or weak grout lines. If it is possible to remove any of the floor material by hand do so, and use that as a starting point for the entire process.
The actual process of removing the tiles is done using a chisel and hand maul. The chisel should be positioned on grout lines, and struck in such a way that you create an opening where you can get at both adjacent tiles. If necessary, a small crowbar can be used to pry up pieces which are particularly resistant.
If you are going to reuse the underlayment found beneath the tile, be very careful not to damage it with the chisel. Once the tile is up, you will probably have to sand down the layer below in order to remove the resistant stone adhesives which are used.
Since removing natural stone is so difficult, sub flooring is often removed and replaced right along with it. This saves time since you don’t have to go slow and worry about damage to this layer. It also means that resistant stone spots don’t have to be chiseled or sanded, as they can just be removed with the bottom level.