Dress in protective clothing with long sleeves, long pants, heavy work gloves and goggles.
Spread the canvas tarp onto the center of the floor. Fold it twice to create padding.
Swing the sledge hammer forcefully to the floor, onto the center of the canvas, to break the tiles at the middle section. The folded tarp should keep the flying shards to a minimum.
Remove the tarp. Take up the shattered tile pieces with your shovel and throw them into the plastic trash can.
Lay the tarp back down and repeat, hitting the floor into pieces section by section. Work your way over the whole surface, getting it all up. Clear out the broken flooring frequently to prevent it from piling up.
Scrape the surface thoroughly with your metal floor scraper to take up the remaining mortar or grout.