To replace a damaged tile you simply scrape out the grout around the tile break up and chip out the tile then scrape off the old adhesive which most likely is thinset a grout like mortar adhesive so you can start over with a clean subfloor surface.
Broken slate tile.
Scrape out as much grout as you can.
This soft stone was formed in ancient seabeds made of clay.
Head over to your local hardware or floor store and select and buy the tiles you would like to use.
Home with slate roofing system.
Drag the narrow flat edge of a small pry bar or a small chisel or along the grout lines surrounding the damaged or lifted slate.
This includes color and texture or anything that you like.