When talking about something, GO OFF means to explode
For example, The fireworks didn't go off when they were supposed to
There was a bomb in the duilding, but it didn't go off.
Since go off means explode, I think we can use it - like expolde - to show emotional reaction
For example, The boss exploded when he heard of the resignation of
the secretary
I hope I answered your question
You can wait for other answers :-D