How to use "never mind "?
My understanding is that it is a phrase means "whatever(rolled eyes)", "even if I tell you, you will not understand", or "neh, I give up to help you understand."
Do I understand it correctly ?
If not, what does it mean and how to use it?

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Personally, I'm NOT familiar with Ilene's second "mind your own business" use or Bramwell's use as reassurance.

Do you still want me to call Dad? 
Never mind, I just got off the phone with him and everything is settled. (neutral statement that something isn't important or needed any more)

I'm here to help. What do you want me to do?
Never mind. You're an hour late and the work is almost all done. (critical)

You can also use "never mind" with other words, usually sarcastically.
"Never mind that I've done this twice as many times as my older brother, he always finds it necessary to give me advice." (I'm annoyed that he gives me advice because I'm the one who has more experience.)

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In addition to Ilene Springer's examples, it is also commonly used in a reassuring way. E.g. somebody has suffered a misfortune or made a mistake and is told "Never mind!" meaning 'don't worry about it'

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Ali--you've got it right.  NEVER MIND means forget it; don't bother me about it.

"Would you tell me the directions to your house again?"
"Never mind.  I'll pick you up."

It can also mean:  MIND (don't get involved in something) your own business.
"Hey, what were you saying about her?"
"Never mind."

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could be that also could be "whatever" like the subject is not important anymore ,

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