Excavate the grout from between the tiles with an angle grinder. Put on a dust mask to keep from inhaling the grinding dust and wear safety goggles to keep flying fragments from entering your eyes. Cut into the grout with the edge of the spinning grinder blade and move the grinder gradually along the grout lines, using medium pressure, to remove the grout.
Place a towel over one section of tile. Strike the tiles through the towel, using a 3-pound hammer, to break up the tiles into smaller fragments. Continue moving the towel to break up subsequent sections of tile.
Pry up the tile fragments with a wide chisel. Holding the chisel at a sharp angle pointed under a tile, insert the blade of the chisel into tile cracks or joint spaces. Tap the back of the chisel with the hammer to drive the blade under the tile fragment, eventually releasing the tile from the subfloor.
Scrape the floor to remove the remaining chunks of mortar, using a floor scraper. For stubborn mortar, saturate the chunks with adhesive solvent for several minutes before scraping or sand them down with an electric sander equipped with a coarse-grit sanding disc.
Sweep and vacuum all the detritus and dust from the subfloor.