Question: In what context are elephants mentioned in the Book of Mormon?

Elephants are only mentioned once in the Book of Mormon in connection with the Jaredites. They were noted as being among the most useful animals. The Jaredites are estimated to have arrived in the New World between 2600 and 2100 BC.

And they also had horses, and asses, and there were elephants and cureloms and cumoms; all of which were useful unto man, and more especially the elephants and cureloms and cumoms. (Ether 9꞉19)

There is no mention in the Book of Mormon of elephants having existed in the New World during the Nephite period.

Wikipedia: Mammoths "were members of the family Elephantidae"

Mammoths could have easily been present in North America at the time of the Jaredites (the only time that elephants are mentioned in the Book of Mormon). The Wikipedia article "Mammoth" notes:

A mammoth is any species of the extinct genus Mammuthus, proboscideans commonly equipped with long, curved tusks and, in northern species, a covering of long hair. They lived from the Pliocene epoch (from around 5 million years ago) into the Holocene at about 4,500 years ago[1][2] in Africa, Europe, Asia, and North America. They were members of the family Elephantidae which contains, along with mammoths, the two genera of modern elephants and their ancestors. ^[1]

Johnson: "Probably it is safe to say that American Proboscidea have been extinct for a minimum of 3000 years"

The Elephant is only mentioned in the Book of Ether. If the elephants had died off at least 3000 years ago, they would still have been well within range of the Jaredite era. Ludwell Johnson wrote in 1952:

Discoveries of associations of human and proboscidean remains [Elephantine mammals, including, elephants, mammoths, and mastodons] are by no means uncommon. As of 1950, MacCowan listed no less than twenty-seven” including, as noted by Hugo Gross, a “partly burned mastodon skeleton and numerous potsherds at Alangasi, Ecuador...There can no longer be any doubt that man and elephant coexisted in America.... Probably it is safe to say that American Proboscidea have been extinct for a minimum of 3000 years." ^[2]

Miller and Roper: "This was long enough to bring them (mammoths) to the time of the Jaredites"

Elephants are only mentioned in the Book of Ether. Wade E. Miller and Matthew Roper note that mammoths survived until the time of the Jaredites: ^[3]

Along with a number of large mammals thought to have become extinct about 10,000 years ago, it’s now known that the mammoth survived for a few thousand years longer. This was long enough to bring them to the time of the Jaredites. A date for a mammoth in northern North America was cited at 3,700 years before the present. ^[4] An Alaskan mammoth was dated at 5,720 years ago. ^[5] In the contiguous United States Mead and Meltzer provided an age of 4,885 years for a dated mammoth specimen. ^[6] As more mammoth (elephant) finds are made, even younger dates will no doubt arise. Generally, when animal species’ populations decrease, they survive longer in southern refugia. Small populations could well have survived in Mesoamerica well past the close of the Pleistocene. The fact that known dates of mammoths in Mesoamerica are numerous up to the end of this epoch helps support this view. It should be pointed out that the mammoth never did range as far south as South America.

Miller favors the Columbian Mammoth as the most likely candidate for the elephant that the Jaredites would have encountered as it it has the closest resemblance to the African and Indian Elephants that they would have encountered if they crossed west asia before making their voyage to the Americas. Its range extends as far north as the Northern United States and as far south as Costa Rica.

Miller and Roper: "Evidence for the survival of the elephant can be found in Native American myths and traditions"

Wade E. Miller and Matthew Roper note that "evidence for the survival of the elephant can be found in Native American myths and traditions": ^[7]

Gulf of Mexico: "giant beasts with long noses that could trample people and uproot trees"

Indigenous people along the northern coast of the Gulf of Mexico have traditions of giant beasts with long noses that could trample people and uproot trees.^[8]

The Abenaki (New England region): "a kind of arm which grows out of his shoulder"

Abenaki tradition tells of a great “elk” that could easily walk through more than eight feet of snow, whose skin was said to be tough and had “a kind of arm which grows out of his shoulder, which he makes use of as we do ours.” ^[9]

The Naskapi (Quebec region): "large ears and a long nose with which he hit people"

The Naskapi people tell of a large monster that once trampled them and left deep tracks in the snow had large ears and a long nose with which he hit people. ^[9]

The Penobscot (Maine region): "huge animals with long teeth which drank water for half a day at a time"

The Penobscot culture hero Snow Owl is said to have gone on a long journey to a far valley in search of his missing wife. When he reached the valley he saw what appeared to be hills without vegetation moving slowly about. Upon closer inspection he found that these were the backs of huge animals with long teeth which drank water for half a day at a time and when they laid down could not get back up. Snow owl was able to trap the large beasts by making them fall on sharpened stakes where he then was able to shoot and kill them. ^[9]

Native American groups from Canada to the Gulf of Mexico

Similar traditions have been documented for Native American groups from Canada to the Gulf of Mexico persuading some scholars that they are based upon a core memory of actual historical encounters with elephant-like species who may have survived into the region as late as 3,000 years ago. ^[10]

Mexico: "long tapering arms and could tear up trees as if they were lettuce"

Pre-Columbian traditions from Mexico tell of monstrous ogre-like giants who once inhabited the region and were subsequently killed following the arrival of Aztec ancestors. These tales attribute some human characteristics to these legendary giants, while other ones seem less so. The giants were said to have long tapering arms and could tear up trees as if they were lettuce. ^[11]

Mexico: "a vague memory of prehensile trunks, something like the `extra arm’ of the Giant Elk in Abenaki and Iroquois myth"

These legends say, notes Adrienna Mayor, “… that the giants destroyed by the ancestors pulled down trees and ate grass, elephant-like behavior.” and she suggests that these stories may reflect “a vague memory of prehensile trunks, something like the `extra arm’ of the Giant Elk in Abenaki and Iroquois myth.” While this cannot be proven, she thinks it possible that “…localized mammoth species (and other large Pleistocene animals and birds) may have survived to later dates in the Valley of Mexico and the Southwestern United States.” … and also that “some aspects of the legendary giant-ogres may have originated in ancestral memories of Columbian mammoths and may have been later confirmed by discoveries of fossils.” ^[12]

See FAIR Evidence:
More evidence of elephants in the Book of Mormon