While most experiments done until now have investigated the effect of calorie restriction, there have also been some more specific experiments.
Some experiments have obtained similar lifespan extension by protein intake restriction, not by energy intake restriction. A few other experiments have obtained the same effect by restricting only the methionine intake.
Methionine is required for the initiation of the synthesis of any protein. When it is insufficient, the rate of protein synthesis slows down everywhere in the body.
Assuming that all these experimental results are correct and that they have a more general applicability than for the few tested animals, then it appears that the lifespan extension is achieved by slowing down the rate of protein synthesis.
This might work by preventing an unnecessary recycling of the body components, which eventually accumulates defects. Nevertheless, in the case of injuries or illness, a reduced rate of protein synthesis is very undesirable.
It is likely that in big or long-lived animals the rate of protein synthesis is already diminished and close to the minimum acceptable, because such animals have lower energy intake per mass needs (even when comparing poikilotherms).
This would explain why such lifespan extension methods do not seem to work in big animals. It is likely that they have low or no effect in humans too.