I think the expression is older than I am.
The only related expression I know is "Can't cut the mustard," and the variation, "To old to cut the mustard." I'd have to do a search to find what it has to do with mustard.
In professional big bands, the rule was "Cut, or no notice." If you couldn't play the part, you were fired with no notice, i.e., immediately.
I think I've seen threads on this subject before. You might try our local search engine.