The flight instructor reported that, during the takeoff roll, shortly after the student pilot rotated and lifted off the runway, there was a loud and noticeable impact to the right side of the airplane. The airplane pulled to the right and they elected to land straight ahead. As soon as the airplane touched back down the right wing struck the runway and the airplane skidded to a stop. Neither the flight instructor nor his student observed the deer that the airplane had collided with before the impact. Following the accident, the flight instructor noted that the right main landing gear had separated from the airplane and the deer that the airplane had impacted was near the runway centerline. A Federal Aviation Administration inspector confirmed that the airplane’s elevator was substantially damaged during the accident.