I have a white marble floor that has been coated with a polyurethane -- the same type that is applied to wood floors. What is the best method to remove the urethane? Can I grind it off or will I need to use a stripper of some sort?

Depending on how thick the urethane is you might be able to grind it off. Grinding can be difficult and can clog your abrasives. The best solution will be to chemically strip the tile. Use a stripper designed for removing polyurethane. Be careful since many of these chemical strippers contain harsh chemicals which are very dangerous to work with. Contact your local janitorial supply house or stone supplier for recommended strippers. This is not an easy job and can get very messy, so be prepared.

TIP There are several “safe strippers” available that can effectively remove urethane finishes. Check with your local hardware store or home center.