Is it correct to say, "Will you do it or NO?"

Solution 1:

Or no is certainly found and without further investigation I wouldn't want to say definitely that it wasn't Standard English. However, or not will raise no objections and for most of us in most circumstances it's probably the safer choice.

EDIT:

Further investigation now complete. The OED has this as its fourth definition of no:

Expressing the negative in an alternative choice, possibility, etc. Chiefly in whether——or no.

There are 14 supporting citations from the fourteenth to the twentieth century, including this, the most recent, from ‘The Times’ of 3 March 1988:

He . . . might afterwards complain (rightly or no) that he was not given an accurate account.

So, yes, it is found in Standard English (but we might still be well advised to use it with care).

Solution 2:

If you write out the two alternatives fully, you get:

Will you do it, or will you not do it?

You can write it without the repetition, and then you keep what differs, which is the not:

Will you do it, or not?

In spoken language it might however be a short form of a different question:

Will you do it, or is the answer "no"?

The pronunciation of the sentence would make that short form possible, but it should be avoided in written language as it can't convey the meaning clearly.