The flight instructor reported that, while demonstrating a soft-field takeoff for a student pilot, he maintained full back pressure with the control yoke; lowered the flaps to 10°; lined up on the wet, grass, 1,900-ft-long runway; and added full power. He further noted that the airplane was not accelerating as anticipated due to the runway condition. The airplane lifted off about two-thirds of the way down the runway, and he decided that the airspeed of 65 mph was "not adequate." Additionally, he saw tall trees at the end of the runway, so he decided to abort the takeoff and land on the remaining runway. He added that he reduced power, that the airplane touched down, and that he applied the brakes but that, "due to the slick conditions," the airplane overran the runway and went down an embankment, and the right landing gear struck a rock hidden by the tall grass. The airplane continued across a gravel road and came to rest in a yard. The airplane sustained substantial damage to the left wing and the fuselage. The instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.