You probably won't have to break any tiles, but at most the first one might break. Just scrape under the tiles and give them a good soak in a tub outside. Pull them out one at a time and scrubs the backs with a brush and then rinse them off. While soaking and letting them dry, scrape off all the compound from the floor. The biggest hit here will be your own labor and time, so the loss is whatever you value that at.