The pilot executed two stabilized low approaches without touching down. After touchdown following the third approach, engine power was added, and the wing flaps were retracted. Before the flaps were fully retracted and before rotation speed, the pilot rotated, and the airplane lifted off the runway. The airplane sank back onto the runway with a side load on the left main landing gear. The left axle broke, and the left wheel separated from the airplane and impacted the horizontal stabilizer. The pilot continued the takeoff, and the control tower confirmed there was no left wheel on the airplane. The second pilot landed the airplane on the runway without further incident. The airplane sustained substantial damage to the left side of the fuselage near the attachment point of the left horizontal stabilizer when the wheel impacted the airplane. The pilot reported that there were no mechanical anomalies with the airplane that would have precluded normal operations.