Hi Chris, Welcome!
You'll first need to establish what type of coating is on the floor. You could start initial clean up with a tile & stone specific high alkaline cleaner such as Stone Tech's KlenzAll. It it's just an acrylic wax the KlenzAll will break up the soil and start disolving the wax. Make sure you mix it to a stronger dilution rate, and allow to dwell on the surface (without drying), and agitate. Vac up residue with wet vac. Rinse, vac, and let dry to see where you're at.
Report back, and we'll guide you home!