A Word A Day tells us the name for locutions such as “Not to mention X“:
paralipsis (par-uh-LIP-sis) noun, plural paralipses (-seez)
Drawing attention to something while claiming to be passing over it.
. . .
Paralipsis is especially handy in politics to point out an opponent’s faults. It typically involves these phrases: “not to mention” “to say nothing of” “I won’t speak of” “leaving aside”
An example from Moby Dick: “We will not speak of all Queequeg’s peculiarities here; how he eschewed coffee and hot rolls, and applied his undivided attention to beefsteaks, done rare.” . . .
UPDATE: Several people pointed out that this can also be called apophasis:
Allusion to something by denying that it will be mentioned, as in I will not bring up my opponent’s questionable financial dealings.
Paralipsis is defined as:
A pretended or apparent omission; a figure by which a speaker artfully pretends to pass by what he really mentions; as, for example, if an orator should say, “I do not speak of my adversary’s scandalous venality and rapacity, his brutal conduct, his treachery and malice.”
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