Mix 1/2 cup mild dish soap with 2 gallons warm water in a bucket. Wet the sponge in the solution and wring it out. Wipe up as much of the spilled or dripped varnish as possible.
Spray the immediate area with the spray solvent and scrub vigorously with the plastic scrub brush. Allow the product to sit for 10 minutes.
Spray the area again and scrub with the brush. Wipe the area with the sponge and let it dry for a few minutes.
Continue spraying and scrubbing with the solvent every 10 minutes until all traces of the varnish are removed. This should only take two or three times at the most.
Use the mop to scrub the entire slate surface. Rinse with clear water and allow the floor an hour or two to dry.