Is there any single term for "Elephants going berserk"? Can we say that the elephant got wild and started destroying whatever is in its path? Is there any term for that? Hope you understand my question...
The elephants rampaged (M-W: Rampage: to act or move in a wild and usually destructive way).
Musth as above is great, but only applies to males, and corresponds to a particular (sexual) context.
Perhaps musth is the word you are looking for:-
An annual period of heightened aggressiveness and sexual activity in male elephants, during which violent frenzies occur.
One would say, "the elephant was in musth".
Why not say the elephants ran amok? Particularly since your question appears not to ascribe this violence to libidinous impulses.
to run about with or as if with a frenzied desire to kill
Wikipedia offers the following description of this phrase:
The phrase is often used in a less serious manner when describing something that is wildly out of control or causing a frenzy (e.g., a dog tearing up the living room furniture might be termed as "running amok.")