Why is finding out mens rea and actus reus so important

I think it is because in order to obtain a conviction both elements have to be present. For example;

1) if a man decides to kill his mother and puts poison in her glass of milk knowing full well that drinking it would kill her. She drinks the milk and dies from the poison.

He clearly had the mens rea (guilty mind), ie he was not legally insane and so knew what he was doing and the actus reus, the poisoning the milk (the act)

Contrast:

2) if a man decides to kill his mother and puts poison in her glass of milk, she, then dies of a heart attack before consuming even a drop of milk he cannot be convicted of her murder.

Again the mens rea was present but not the actus reus for murder. (Notwithstanding the fact he would probably be charged with attempted murder).

So in essence you have to identify both the guilty mind and the guilty act for the crime in question.

There is some case law about someone bashing someone on the head and believing them to be dead throws them off the edge of a cliff. The victim was not dead and in fact died days later of exposure or something. So the question was can you have the mens rea necessary for murder when you believe the victim is already dead. I don't recall the outcome or the case name so not much help but it makes for interesting reading.