A Google search on that verse teaches me that the meaning is "Do not eat with such a person". You are quoting the King James Bible, which, although it contributed greatly to the English language, does not always use vocabulary or constructions that are immediately recognizable or easy to identify.
With such an one no not to eat.
"an" seems strange, I would use "a" in this case.
"such a one" is a person as described in the preceding phrase.
I would read "no not to eat" as
No, (you are) not to eat (with such a person).
So it becomes something like
With such a one (= such a person), no, (you are supposed) not to eat.