This idiom or expression has to do with:

Losing one’s mind.
Becoming irrational.
Losing touch with reality.
Acting in an angry manner.

A. I know I haven’t known her long, but I love her. We want to get married and go traveling.
B. Well, I’m happy for you, but use your head! Don’t be going off the deep end!

Also:
Jumping off the deep end.