I heard someone say this recently.

Problem:
This sometimes is a mispronunciation of another idiom.

Explanation:
The other idiom is “It doesn’t cut muster.”

The noun “muster” means an assembly of military troops for inspection.

The verb “cut” in the idiom refers to “making the cut” — that is, “meeting a certain standard, below which whatever is being inspected is cut”.

So “It doesn’t cut muster.” means that something does not meet a certain standard following inspection.

Given that the noun “muster” is not as commonly used as the noun “mustard”, I suppose that it is not surprising that some say or write the idiom as “It doesn’t cut mustard.”

For fun, I searched Google — with the quotation marks included in the search box — for “doesn’t cut mustard” and “doesn’t cut muster” and got about 61,700 and 1,070 matches, respectively.

According to a post at Washington State University’s website, “cut the mustard” first appeared in a 1902 O. Henry story and was used there to mean to achieve the required standard.

Solution:
“It doesn’t cut muster.” or “It doesn’t cut mustard.” — your choice! Simply be conscious about which one you’re using — and why!