Flight Instructor with student reported the student pitched up excessively and applied too much rudder causing the aircraft to stall during the takeoff roll. The instructor took control; but was unable to recover and the aircraft departed the runway.

Narrative

Dual local flight. Departed south west to ZZZ; had student under the hood for Basic Attitude Instrument Flying (BAIF) maneuvers. Vectored him over ZZZ to overfly the field to verify wind conditions. Finished Instrument work in the practice area and told student to head into ZZZ. I simulated an engine failure 4 NM out at 4000 feet to test student's decision making. They were able to successfully perform an emergency approach to Runway XX within standards. We stayed in the pattern to practice soft field takeoffs and landings. I had demonstrated one departing ZZZ1 and allowed the student to try one after back taxiing. I was anticipating needing to help the student quite a bit since they had previous issues with pitching up too high on takeoff due to them staring at the PFD and not looking outside. Sure enough; the Student attempted to pitch up way to high to force the aircraft to fly before it was ready for even ground effect. I took controls as the student kept drifting too far off centerline. I explained the issue during the traffic pattern and we came around for a normal landing. which was slightly flat. Back taxi again for another soft field takeoff attempt; where I assisted the student a bit to show them again how they need to hold the pitch and then to immediately get the nose down once we are airborne. I eased off the controls to see if he could add the contiguous forward pressure as we had discussed and demonstrated. Student again drifted off to the left and I had to help them back to centerline and hold them in ground effect. One more lap and we did another landing and back taxi. This time I emphasized needing to pitch the nose down again once we lifted off in ground effect; and wanted to see if the student could act more independently this time and fix the excessive pitch. Initially he did alright and seemed to respond more to my occasional calls for more rudder usage. But once again he got jumpy and yanked back on the yoke. At this point things happened too quickly and I noticed he pushed a bit too much right rudder causing a huge wing dip. This briefly froze me for a moment to try and process what I just saw off the wing; and I did not fully try to overpower the student to fix the situation; but I did remember reaching for the controls as I heard the stall horn. At this point the plane was basically stalled and there was not much I could do to stop it from veering off the runway. So I opted to level the wings and ease it back to the ground wherever the nose was pointed at that moment as any attempt at massive control inputs would likely have made the situation worse. We went of the runway; missing a runway light by inches I'm guessing; and then rolling out into the bean field to the right of the runway. I took a moment to collect myself in the situation; then shut down and called the school. I dropped my guard to try to let the student figure out the soft field takeoff when they clearly needed additional assistance to figure out the maneuver. Additionally; the student definitely has an over reliance on the PFD and was not looking outside for the takeoffs; causing them to consistently pitch up too high. I had told them both to look for bringing the nose to the horizon and roughly 8 degrees of pitch up; and they focused on the attitude indicator and not the outside sight picture.Do not get out of the close in defensive positioning behind the yoke until I am certain the student can correctly control the aircraft to lift it off and then pitch down to stay in ground effect. Ensure the student is utilizing the correct sight picture by looking outside and not staring at the PFD for takeoff.