The 1874 RLDS edition accidentally replaced or with and. The 1908 RLDS edition restored the original or to the RLDS text. There are other instances of “without X or Y” in the text, and two of them are found in nearby verses:
There is one example in the text of “without X and Y”, namely in Mormon 5:16: “and they are without Christ and God in the world”. Of course, in this instance, the scope of negation includes both Christ and God; thus the and is appropriate in that passage. As we might expect, the Book of Mormon uses and to connect beginning and end when the conjunctive relationship is positive rather than negative:
But there are no examples of “without beginning and end”. Given the negative preposition without, the conjunction or is undoubtedly the correct reading for Alma 13:8.
Summary: Maintain the coordinating conjunction or in Alma 13:8 (“without beginning or end”).