I've read a sentence which stated as " It does no good to get upset.." . Can this sentence be "It does not good to get upset"??
No, it can't. In this case, 'no good' expresses a quantity of 'good'.
Here we have the important fragment for this sentence: "It does no good to get upset." What are we doing by getting upset? We're doing good. How much of it? None at all.
Another way to render the sentence is "It doesn't do any good to get upset," with the same meaning.
'Not' would instead express that 'getting upset' isn't good, which we could render "It's not good to get upset," which people would understand as having essentially the same meaning.
I would like to suggest; The words "doing good" cannot be quantified nor numbered. You could say, for example, " It does no good." but "It does not good." would be an archaic construction conveying that it did in fact do evil.
You may say that this answer is no good. In that it does not answer your question, or that this answer is 'not good', in the sense that it was not what you wanted to hear, or it carried unwished for consequences.
Bear in mind, the original sentence includes an element which is "understood". It does no good ( to anyone ) to get upset. The element of doing good is not quantifiable.
Also consider. 'It is no your business.' This may well be said in Scotland, 'It is not your business ( to say, interfere etc.)' may well be said in England in very specific circumstances, and 'It is none your business' would be more usually expressed as, 'It is none of your business.' English has usages which provide for many nuances of meaning.