The pilot was receiving flight instruction in the tailwheel-equipped airplane that he had recently purchased. The pilot stated that the airplane bounced slightly upon touchdown, but he corrected by increasing engine power and a normal landing was made on the runway heading. The pilot reported that during the landing roll he heard his flight instructor ask him to “cut power” multiple times. The pilot stated that he responded by slowly pulling the throttle control aft while he maintained directional control as the airplane decelerated. The pilot reported that his flight instructor continued to tell him to “cut power” in a more urgent tone. The pilot stated that he confirmed the throttle control was already full aft before he applied wheel brakes to “expedite the stop” instead of letting the airplane continue to coast. The pilot stated that when he applied wheel brakes the airplane nosed over. The fuselage, rudder, and the left wing were substantially damaged. The pilot reported no mechanical malfunctions with the airplane that would have precluded its normal operation.