Oliver Cowdery’s initial cut was probably a simple misreading of the original manuscript (which is no longer extant here). The words cut and cast are visually similar, and both are semantically acceptable here. Moreover, Oliver’s correction has the same level of ink flow as the surrounding text, so the correction seems to have been virtually immediate.
Another place in the text where cut and cast were mixed up occurred when the 1830 compositor was setting the type:
In this particular instance, the change was in the other direction: an original cut was accidentally replaced by cast.
Overall, the Book of Mormon text, when referring to one being either cut off or cast off from the Lord, has 28 occurrences of “cut off ” and 15 of “cast off ”. In this count, I exclude a number of cases found only in biblical quotations in the Book of Mormon (these King James quotations consistently use “cut off ”). The main point here is that for all these nonbiblical cases, either “cut off ” or “cast off ” is possible. Thus in each instance we follow the earliest textual sources in determining whether we have a case of “cut off ” or “cast off ”.
Summary: Retain in 2 Nephi 30:2 the verb cast (Oliver Cowdery’s virtually immediate correction in 𝓟).