Some other points to add to this discussion:
1 my understanding is that some aircraft mixture cables are significantly less thick than throttle cables as they are not designed to be used in the same way. Thus the risk of snapping the mixture cable is greater than with a throttle cable.
2 in discussions with a two CAAFU examiners and the CFE on this very topic last year, it appeared that the CAA did not condone the practice of using the mixture to simulate an emergency because of the very real chance of that practice becoming "for real". In the same way you would not give the student an "engine failure" in a single by removing the magneto keys.
3 regardless of the desirability of giving the student a "realistic" emergency, it is necessary to be aware of your responsibilities as an instructor. IF there was an accident as a result of mishandling, not only would you be in the firing line for a CAA prosecution under articles 63 and 64 for endangering, but if the student was injured you would very likely be the target for a civil action for negligence. Electing to carry out a non-approved procedure which leads to injury would be likely to invalidate your insurance policy and that of the school. I am aware of several cases where prosecutions have been successful and these have been followed by claims against instructors or pilots, which cost them large sums of money in legal fees not to say the wards made by the courts.
In these increasingly litigious times it is best to stick to what the book says and not take any unnecessary risks.
Safe flying!!