It wasn't that long ago when both the very experienced flying instructor (30,000 hours)and his very experienced Boeing 767 captain "student" were both horribly burnt when the Duchess they were flying clipped trees shortly after take off and crashed at Camden. Both survived the wheels up landing but the instructor died of burns when the aircraft went through a fence and hit an iron girder part of farm machinary and caught fire. It was a "simulated" engine failure caused by a deliberate mixture cut. There is no shortage of documentary evidence that mixture cuts to simulate engine failure after lift off have caused fatal accidents.
Many years ago the NTSB warned of the dangers on simulated engine-out manoeuvres in a Bulletin that (edited for brevity) stated " The fatal crash of a light twin in which a flight instructor and an applicant for a multi-engine rating were killed prompted the NTSB to issue an urgent warning to all pilots simulating an engine-out condition on multi-engine aircraft...the boards investigation revealed that some flight instructors do use the mixture control or the fuel selector to shut down an engine to test a multi-engine applicant..
...the urgent warning was aimed at flight instructors who were using this procedure at altitudes too low for continued safe flight..the NTSB observed that use of such procedures at traffic pattern altitudes may not permit instructors enough time to overcome possible errors on the part of the applicant...
....the recommendation by the NTSB means that all simulated engine-out operations at the lower altitudes should be accomplished by retarding the throttle and this should be done slowly to avoid engine damage or failure...this careful technique will protect the engine, and at the same time provide for instant power if it is needed.
Any instructor that uses the mixture control to simulate an engine failure after take off is should be charged with reckless conduct.