Looking at the “Big List” entry for “Cut the mustard”, I was wondering if there is any evidence for the “cut” to be “cut” as in dilute or weaken “he cut his whisky with water”, the sense being that it would be difficult to have much effect on the powerful taste of mustard?

I know of no evidence supporting this notion, and one fairly strong piece of evidence against it:  based on OED cites, “cut the mustard” (1905) antedates the use of “cut” to mean “dilute or adulterate” (1930).