Joe jumped off a cliff and died.

[Jokodo]

How is the idea expressed in classical propositional logic that one event caused another one event?

For example:

Joe jumped off a cliff and died.

Please read the question carefully. Please don't go into the usual wild and nonsensical answers most people here usually do.

If you understand both English and human deductive logic, it should be a piece of cake.
EB

This is not the expression of an idea. This is the statement of two facts, which may or may not be connected.
In logic, this would be written:

A and B

If you wish to assign causality, you would write it as

A -> B

...which in English would be "if Joe jumped off a cliff, then joe is dead".

That's still not causality, just material implication. Consider three probably true statement "if a planet has free oxygen, it had life": oxygen does not cause life, indeed, for primitive life forms it is deadly being as it is highly reactive. To the contrary, life is the only plausible source of free oxygen.

Similarly, if the antecedent can not possibly be true, for example because it contains a contradiction, the implication also holds. "If 1=2, Joe is dead" is true, and so is "if 1=2, Joe lives forever" - since there cannot be a scenario that contradicts it, as the antecedent cannot be true. But paraphrasing this as "1 being 2 causes Joe to be both dead and alive" seems awkward at best.