Don't stress の意味は？

Not exactly right.

Don’t stress about it.
= Don’t feel stress about it.
= Don’t worry about it.

What should I bring to John’s party?
Don’t stress about it. He’s got everything.

What time do I call the office?
Don’t stress about calling. They will call you.

I’ll come back here to return your $10. Are you gonna stay here until 5?
I’ll probably be gone by then. Don’t stress about getting back here today. See you tomorrow!