Remove all items from the floor to gain access to the slate tiles.
Put on safety glasses, rubber gloves and knee pads. Open windows in the room to provide ample ventilation.
Mix wax-stripper and water in a bucket according to the wax stripper manufacturer's directions.
Dip a large sponge or sponge mop into the wax stripper. Wring the sponge or sponge mop, leaving the sponge or mop saturated but no longer dripping.
Swab a 4- by 4-foot section of the floor with wax stripper beginning in a corner of the room. Let the wax stripper remain on the floor for 10 to 15 minutes, depending on the brand of wax stripper. If the wax stripper begins to dry, apply a second coat of wax stripper over the first to keep the area wet.
Wipe the floor with a rag to remove the gummy wax. Turn the rag frequently to a clean area, and continue rubbing the slate tile. Reapply wax stripper if any wax remains on the surface. Floors with several coats of wax may require two or more applications of the wax stripper to remove the buildup.
Move to an adjacent 4- by 4-foot section of the floor. Apply the wax stripper with the sponge or mop, let it sit and then wipe it off with a rag. Continue to move section-by-section across the surface of the flooring, removing wax until no wax remains on the floor.
Mix 1 tablespoon of mild dish soap with 1 gallon of warm water in a bucket. Submerge a clean sponge or mop into the water, and then wash the slate tiles.
Empty the bucket and rinse it well. Rinse the sponge or mop to remove all soap residue. Fill the bucket with water, and wipe the floor two to three times.