At about 14:30 EST, a Beech Duchess was substantially damaged during the takeoff roll at Cincinnati Municipal-Lunken Field. There were no injuries. It had rained earlier and the runway was still wet. During the takeoff roll, the instructor allowed the airplane to accelerate, and pulled back the mixture to the left engine at approximately 30 knots. The airplane veered to the left about 30 degrees. The student did not retard both throttles immediately, so the flight instructor advanced the mixture on the left engine. However, the corrective action was too late. The airplane went off the runway and into the wet grass, then ran into an elevated asphalt driveway at 10 to 15 knots. The nose gear collapsed, and the airframe was bent.