By sarcasm I mean an ironic statement which is, in its non literal meaning, meant to undermine.
Irony means the opposite to what is said; it can have different meanings in the same context. e.g. the opening of Pride and Prejudice
It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.
can be read as ironic, but only if we abandon the economic norms involving bourgeois marriage.
Are there any problems with sarcastic statements which address who we are undermining and are meant to be misunderstood by them? These seem to fail to mean unless misunderstood, which seems, if not paradoxical, then at least strained.
It seems to me it would belong to something like the liar sentences. I think that such an insult expresses something which isn't made sense of. Which looks a bit like the liar paradox: that this expression makes no sense is true.