The student pilot reported that he rotated about 60 knots to a nose up attitude during takeoff. He said that the left wing raised “abruptly” due to a wind gust. He stated that he over corrected with left aileron and “set the plane back down on the runway.” The airplane was then heading for the edge of the runway and the pilot reduced the airplane throttle. The airplane exited the runway, its safety area, and nosed over in a plowed field. The pilot reported no mechanical malfunctions with the airplane reference the accident flight.