C172 pilot reported engine failure while maneuvering. Pilot diverted and performed an off-airport landing.

Narrative

Initiating lesson plan for syllabus; was out in the practice box working on slow flight- into simulating a power off stall. From slow flight I pitched for 65knots with a 500 FPM descent and became to pitch up until I heard the Stall warning horn. In my Recovery of going Carb heat in; full throttle; and flap 20 my airplane engine began to sputter and the propeller began to windmill. I went Mixture full rich and the airplane propeller never caught and I came into a descent where the airplane wouldn't climb anymore. From there I broke out the emergency engine out checklist and did the following floor to door; Fuel Selector both; check mixture in; flaps up and tried trouble shooting the ignition and checking engine instruments. When I realized nothing was working I decided to preform an Engine out forced landing. I called XXX.X ZZZ1 airport and squawked XXXX; they informed me to try to get a hold of ZZZ CTAF and see if I could make it to the runway. I secured the engine; turned off all the gas; turned off the magnetos; and master and prepared for impacted unlatching the door. I glided about a mile SE of runway XX and landed soft-field in a field.