The pilot reported that he was landing following a cross-country flight that originated from the same airport earlier that day. During the landing touchdown and using flight control inputs to compensate for a crosswind, the airplane bounced. The pilot let out the rudder correction and the nose swung to the left. The wind got under the left wing and lifted it. The pilot attempted to correct by inadvertently using right aileron and right rudder when he should have used left aileron and right rudder. When the airplane touched down again it went off the left side of the runway. The airplane received substantial damage to the engine mount. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operations. At the time of the accident, the pilot was landing the airplane on runway 18 with wind from 100 degrees at 8 knots. The pilot reported he should have just performed a go-around.