The Lycoming Flyer Key Reprints 1992 on page 49 has this brief (slightly edited for brevity) warning by the US NTSB.
"The fatal crash of a light twin in which a flight instructor was killed prompted the NTSB to issue an urgent warning to all pilots simulating an engine-out condition on multi-engine airplanes.
The Board's investigation revealed that some flight instructors do use the mixture control or fuel selector to shut down an engine to test a multi-engine applicant. Although this is a recommended procedure, 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 all simulated engine-out operation at lower altitudes should be accomplished by retarding the throttle and this should be done slowly and carefully to avoid engine damage or failure."
One presumes the term "lower altitudes" used by the NTSB covers simulated failures after lift off and below circuit height?