The flight instructor and student were conducting full-stop landings in the tailwheel-equipped airplane. The flight instructor reported that the wind was calm throughout the local flight in the traffic pattern. During the final landing, upon touchdown the airplane swerved about 60° left of the runway heading. The flight instructor immediately took control of the airplane, but it swerved 90° to the right and departed off the right side of the runway. At that time, the flight instructor believed that the airplane had sufficient airspeed of 35-40 mph and an open grass area ahead to safely takeoff. However, the airplane entered an area of waist-high grass about 60 yards before a chain link fence that resulted in increased drag on the airplane. The flight instructor reduced engine power to idle shortly before the airplane struck the fence and came to a stop upright in a soybean field past the fence. The airplane’s wing struts and an engine mount tube were substantially damaged during collision with the fence. The flight instructor did not report any preimpact mechanical malfunctions or failures that would have precluded normal operation of the airplane.