Это вроде "don't get crazy", нет?
Да, похоже на то.

Максим, crazy vs mad тысячу раз обсуждалось в интернете. Гугл в помощь.
Basically (North American English):
mad = angry;
crazy = weird, doing weird things, looking mentally ill, sometimes awesome, etc.

So 'не сходи с ума' is closer to 'don't get crazy'.
An example:
A boy has fallen in love with a girl and tells his mom: 'I'm going to go ahead and buy her a parrot. Maybe that will make her begin to notice me.'
She answers 'Come on, don't go crazy, she's dating with Ronny and he's the big shot there in your sand-box with his quad. That's not gonna be a great blow to her.'

Don't get mad (aka don't get angry) = не злись/не кипятись/не психуй/
also: хорош/расслабься/остынь. (relax, calm down)