The flight instructor of the multi-engine, retractable landing gear airplane reported that, while conducting a touch-and-go landing with the student pilot at the controls, during the landing roll, the student pilot intended to raise the flaps, but instead raised the landing gear lever from the down to the up position. The right main landing gear retracted, the right wing impacted the runway surface and the airplane veered right. The flight instructor observed that the landing gear lever was in the "up" position and immediately put the lever to the "down" position. The left main landing gear partially retracted, and the airplane exited the right side of the runway. The airplane sustained substantial damage to the rudder. The flight instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.