The flight instructor reported that during a dual training flight with a student pilot, they returned to their base airport and practiced two landings without incident. During the third landing, the student pilot applied too much elevator back pressure in the landing flare, and the instructor stated “power.” Subsequently, the student pilot applied full power to go-around, instead of a “slight amount of power” which was what the flight instructor expected. After the application of full power, the airplane drifted beyond the right side of the runway, was near the aerodynamic stall speed, and was approaching trees ahead. The flight instructor reported that she “eventually” was able to take the flight controls, where she reduced power to idle, lowered the nose of the airplane, and landed in a down sloping grass area beyond the end of the runway. During the runway excursion, the airplane impacted trees, which resulted in substantial damage to the right wing and fuselage. Neither pilot reported any preimpact mechanical malfunctions or failures that would have precluded normal operation with the airplane.