Deut. 18:15, in warning those who would not hearken to the future prophet (Christ) that the Lord would raise up, the punishment in verse 19 is that the Lord "will require it of him." But Acts 3:23 warns that the non-hearkeners "shall be destroyed from among the people,"which is much closer to 3 Nephi's warning that such rebels "shall be cut off from among the people." Sure, it seems like a case of clumsy and ignorant plagiarism.
More than twice, actually. 3 Nephi 21:11 speaks of those who will reject the Gospel of Christ and warns that "it shall be done even as Moses said," namely, "they shall be cut off from among my people who are of the covenant." Not just having some "required of him," but the more serious "cut off" from among the people, or in this case, "from among my people." 3 Nephi 21:20 again warns that the rebellious shall be "cut off from among my people." Now all these 3 Nephi passages could be lumped together and one could argue that Joseph just had that phrase in his head at the time and used it repeatedly during that day or week or writing. But how do we account for First Nephi passage that was probably widely separated in time from 3 Nephi's translation? Didn't it ever occur to him and his scholarly co-conspirators to look up Deuteronomy rather than Peter for a quote from Moses? Sloppy, sloppy, sloppy. And puzzling.
In fact, this is the kind of puzzle that ought to stir some thinking. The change in language from Peter and the persistent use of "cut off" in the Book of Mormon is not consistent with the sloppy plagiarism charge. So what is going on? Great question! Good questions with an open mind and some patience are often rewarded with interesting answers.
There's a further question that students of the Bible might also wish to ask: "Why did Peter himself use language so different from Deuteronomy 18?" It turns out that Peter's paraphrase does not follow the Septuagint in this case, so Peter appears to be departing from both the Greek and Hebrew texts. Why?
A possible answer to these questions, with interesting implications for the Book of Mormon, can be found in the Maxwell Institute's publication, Insights, Vol. 27, No. 5 (PDF file), in the article on page 3, "The Prophet Like Moses" by John A. Tvedtnes and E. Jan Wilson. I recommend the PDF version to see the Hebrew more clearly, but an HTML version of the article is also available. There is a lot of detail in this short article, but here's one passage with one of the main points:
Based on analysis of the Hebrew in Deut. 18 and several relevant passages elsewhere, a plausible case can be made that the original Hebrew may have read "cut off" instead of "require it" and referred to being cut off "from among the people" or "my people" instead of "of him." Rather than both Peter and Joseph being sloppy in their quotations of Moses, there's a reasonable case that Peter was informed by an ancient Hebrew source using language that differs slightly from the current Masoretic text, language that appears to be consistent with language uses consistently in the Book of Mormon. As for the Book of Mormon's version of Deut. 18, are we dealing with a terribly sloppy but very lucky blunder by a con-man who inexplicably looked up and kept using Peter's words when attempting to quote Moses, or are we dealing with an ancient text prepared by scribes whose version of Deuteronomy on the brass plates led them to understand Deut. 18 in much the same way that Peter did?
In light of intelligent questions coupled with scholarship, the way the Book of Mormon quotes Moses in Deuteronomy 18 is certainly interesting. What initially looks like a blunder upon further examination becomes an inexplicable blunder ("how could anyone be so stupid and sloppy?"), then a puzzle, and then an interesting find where a former weakness may actually be a strength. It's a small thing and is certainly no reason to run off and join the Church, but it's hardly a reason to leave.