One says that something is "off the mark". For instance, an opinion or comment. But when it is way off, why is it "wide of the mark" instead of "wide off the mark"?
"Wide of the mark" is an established phrase, using a meaning of "wide" that is rare today — notably still used in cricket, where a "wide" is a ball that was bowled outside the permitted target area (the wicket).
"Off the mark" is also established phrase.
"Wide off the mark" is not natural, because the relevant sense of "wide" is now used only absolutely ("went wide") or construed with "of". OED lists only "from" as an alternative, and marks it obsolete. I think it would be taken as an error for "wide of the mark". "Far off the mark" is more natural, but I don't recognise it as an established phrase.
[Edited to correct two points challenged in the comments: that "Off the mark" is an established phrase, and that the sense of "wide" is in wider(!) use than I said, though still restricted.]
"Wide off the mark" is incorrect and I would say that is because wide doesn't tell you about distance (like "far" does), it tells you about size. After all, you can't say "big off the mark" either, can you?
When you say "wide of the mark" you are using "wide" to mean not "of a great size from side-to-side" but "to the side of". Incidentally I don't think you should take it to mean that it is far off target: even a near-miss is wide of the mark, so the sense is not quite the same as "far off the mark".
"Wide of" is used quite frequently in this way: for instance, footballers are forever hitting shots wide of the goal. (That's round-ball football by the way, not the American sort...) There is also the specific cricket-specific sense of "wide" which Colin Fine has mentioned, which seems to have the same sense of "to the side", but in that context has even got to the point where you can talk about "a wide", making it into a noun.
here's one possible explanation
They both work. I think "of" is more common. It's like "clear of the mark."
"Off" would be more like "far off the mark."
Grammatically, I think "wide of the mark" is adverbial, as in "I placed it west of the mark."
"Wide" answers the question "where," and the prepositional phrase "of the mark" modifies "wide."
With "wide off the mark," I think the prepositional phrase answers the question "where," and "wide" is adjectival, modifying the prepositional phrase.