The original text had two that ’s surrounding the phrase “in the name of God”. In his editing for the 1837 edition, Joseph Smith deleted the first one, which therefore implies that the phrase “in the name of God” refers to the verb say —in other words, “I say in the name of God that … ”. The 1837 edition deleted the wrong that, thus producing “I say that in the name of God ye shall be struck dumb”. All subsequent printed editions have followed this reading, even the 1908 RLDS edition (which normally relies on 𝓟 for establishing the text).
In this sentence the phrase “in the name of God” acts as part of the performative verb say. Performatives are verbal actions that perform an act by uttering some words (such as “I sentence you to ten years in prison”). In many instances, performatives also involve a statement of authority by the individual uttering the performative: “by the power vested in me / I pronounce you man and wife”. In Alma 30:49, the performative verb is say, and therefore “in the name of God” is semantically attached to say (in accord with how Joseph Smith edited the text for the 1837 edition). Similar examples of performatives in the Book of Mormon include the following:
The critical text will, of course, restore the repeated that here in Alma 30:49 since that is the earliest reading. For other examples of that ’s surrounding prepositional phrases, see under 2 Nephi 1:17. For a more general discussion of the repeated conjunctive that, see under that in volume 3.
Summary: Restore the repeated that in Alma 30:49: “I say that in the name of God that ye shall be struck dumb”; the current reading, “I say that in the name of God ye shall be struck dumb” changes the nature of the original performative and is apparently the result of accidentally deleting the wrong that when setting the type for the 1837 edition.