Mormons have answers to pretty much every objection. Not saying these are right, but:
Disappearing Breeds
Here is a list of Mormon animals that might have existed but whose remains disappeared:
1. Elephant The only place where elephants are mentioned in the Book of Mormon is in Ether 9:19 which was written in approximately 2500 B.C. Thus any elephants existing upon the American continents need not have survived past about 2400 B.C. While the jury is still out, there are a number of North American Indian traditions that recount legends of giant stiff-legged beasts that would never lie down, had a big head and large leaf-like ears, round footprints, forward bending knees, and had a fifth appendage coming out of its head.8 In addition to the legends, five elephant effigies have been found in ancient Mexico and two in Arizona.9 Scientists agree that mammoths and mastodons once inhabited the Americas, and an article in Scientific Monthly, entitled “Men and Elephants in America,” suggests that these proboscidean animals (elephants, mammoths, mastodons) may have survived in the Americas until 1000 B.C. — well within the time frame demanded by the Book of Mormon.
2. Horse. There have been a number of horse bones discovered in America that might date to Book of Mormon times. The surviving remains from such finds are currently undergoing testing to determine their antiquity.11 Misnomers and Other Namesakes Here is a list of New World animals that might have been re-labeled by the Nephites:
1. Cattle and Cows. The term “cattle” is used three times in the Book of Mormon (Ether 9:17-19; Enos 1:21; 3 Nephi 3:22), while the term “cow” is used twice (Ether 9:18; 1 Nephi 18:25). The Jaredite record is unclear as to whether “cattle” and “cows” are the same animals, or if “cows” are a subcategory of “cattle.” When the Miami Indians, who were familiar with cows, first encountered the unfamiliar buffalo they simply called them “wild cows.” Likewise the explorer DeSoto called the buffalo “vaca,” which is Spanish for “cow.” The Delaware Indians named the cow, “deer,” and a group of Miami Indians labeled sheep, which they were unfamiliar with, “looks-like-a-cow.”12 2. Horse. Could the Nephites have used the term “horse” for deer or some other animal? It is not impossible considering the above examples. Figurines, for example, of the pack bearing South American alpacas — which are related to the camel — have been unearthed as far north as Costa Rica.13 An early pre-Spanish incense burner discovered in Guatemala shows a man riding on the back of a deer. A stone monument dating to 700 A.D. shows a woman riding a deer. Another similar figurine was found in central Mexico, and until recently, many people in Siberia rode on the backs of deer. In such cases the deer served as “horses.”14
Hunting for Elephants in the Book of Mormon Book of Mormon “Anachronisms” Part 1: Fauna, Animals