No, not a left-handed drill. Using a High Speed Steel or carbide tipped drill, you drill a small hole into the centre of the screw (or bolt as you have called them) sufficient to use a stud extractor to wind them out. It will be difficult to get it centralized so take your time and get it right. It is the stud extractor that has the left handed spiral. The diameter of the hole that you drill needs to accommodate the stud extractor which is a tapered spiral. Insert the extractor into the hole you have drilled and wind it out using the proper handle on the extractor.
Get some new replacement screws and don't overtighten them next time.
ChicksFan
January 2010