The flight instructor reported that during an instructional flight, he was conducting a high-speed taxi exercise on the runway with a student pilot, to work on rudder control. He instructed the student to remain at or below 50 mph and that they would begin slowing the airplane about 1,000 ft from the departure end of the runway. About halfway down the length of the runway, the instructor noticed that the airspeed seemed high, and he informed the student that they needed to decrease the airplane’s speed; however, the airplane continued to accelerate. When the instructor told the student to begin their deceleration, the airplane did not decelerate as expected. As the airplane overran the runway, the instructor took the flight controls and elected to take off. The airplane was flown to the originating airport, where substantial damage to the horizontal stabilizer and elevator was discovered during postflight inspection, which resulted from impact with a runway end light during the runway excursion. The instructor reported that there were no preaccident mechanical malfunctions or failures that would have precluded normal operation.