A Flight Instructor reported a stuck throttle and return to departure airport.

Narrative

We were practicing takeoff and landings with a private pilot student. On the 7th takeoff in the pattern; student regularly turned crosswind and downwind at full power on the climb to 800ft (pattern altitude). Student tried to level off at pattern altitude and manifested throttle was stuck at full power. At that point; flight instructor (me); took the flight controls; and verified throttle was actually stuck were student manifested. After several tries and inputting a lot of strength; I managed to bring the power down to 1800 RPM's. Informed tower about the issue and asked for an immediate landing on rwy XXL; full runway length. After realizing that even with all the strength I wouldn't be able to bring the power back to touchdown setting (regularly given in power to idle conditions); I decided the best course of action was cutting the mixture; that way we would have a loss of power; hence a loss of thrust and have a safer condition for the landing. After managing the altitude and airspeed as much as I could using flaps and different angle of attack configurations; we were set on a stable faster than normal approach; already onto gliding distance to the runway. After crossing university drive and already over displaced threshold; I fully leaned the mixture; causing a total loss of power on the engine; hence a loss of thrust and airspeed on the aircraft. A completely safe landing was executed on rwy XXL; and thereafter I was able to exit the runway safely. Once out of the runway; I pulled the throttle back with both of my hands and was able to bring it back to fully idle position. We were able to restart the airplane and safely taxi back to the ramp.