Reading an old magazine (Smithsonian of May 1998), I came across the following text in an article about the Mexican Tarahumara natives:
"In the 1890s, Carl Lumholtz was told a legend about a race of giants ("as big as pine-trees") that had occupied the canyon country when the Tarahumara arrived. The giants ate the Tarahumara children and ravished the women. At last, the people exterminated the giants by tricking them into eating a mixture of corn and a poisonous extract from the chilicote tree." 
These are interesting giants which despite being as tall as trees are sufficiently nimble to have intercourse with human women. So maybe they were giants in a metaphoric way, but size-wise they were like us.
Giants, from my perspective mean "different humans", such as Neanderthals or Homo erectus; they were the way that ancient cultures declared that a group of people were not Homo sapiens, they were men, but not like us, they were hominins. So I decided to find what Lumholtz had written about them, and below is what I found.
Giants and Tarahumara natives
Carl Lumholtz was a Norwegian explorer who travelled to Australia and Mexico. He spent many years in Mexico between 1890 and 1910, during which he spent a full year with the Tarahumara people. His book, Unknown Mexico is the source of the Giant's myth quoted below:
On the heights once lived giants. They were as big as pine-trees and had heads as big as bowlders [sic]. They taught the Tarahumares how to plant corn, by cutting down trees and burning them, but they ate children.
A woman bore a giant in a cave, which was situated very high up on the side of a valley. She died, because the child was so large, and he was taken care of by his grandmother. Once when she was asleep, she turned over and crushed him.
From Wasivori (near Cusarare) came giants to Nararachic to ask alms. Tesvino [Note: a kind of beer made from corn] they liked very much. They worked very fast, and the Tarahumares put them to hoe and weed the corn, and gave them food and tesvino. But the giants were fierce, and ravished the women while the latter were under the influence of the Moon; therefore the Tarahumares got very angry and they mixed a decoction made from the chilicote-tree with the corn that they gave the giants to eat, and the giants died.
The paragraph before the one quoted above mentions a "Deluge", which filled the world with water. It, like most Flood myths around the World (and also in the Americas) must surely reflect the deep impression caused by rising sea levels and glacial dam ruptures with the consequent flooding caused by climate change at the end of the last Glacial Period some 8 - 10 kya.
This suggests that Giants (Neanderthal) were alive at that time, in America.
These giants evidently caused problems to the human mothers bearing them, but I don't think that size was the issue (the baby's grandmother crushed the infant in bed while sleeping next to it... it wasn't a gigantic baby, it was probably a big headed child).
They were farmers but ate human children and raped their women. They lived in the mountains (perhaps in caves?), and their interactions with humans were not amicable. But, from the mythic point of vies, these creatures were not gods either, poison killed them (a tea made from the beans of Erythrina flabelliformis), they were "men".
More recently Guadalupe Holguín (2011) , mentions these giants as part of the "Collective memory" of the Tarahumara. They were known as "Ganokos" and were alive between 1,500 BCE and 300 CE. She mentions a giant which was known as a "uribi", which lived in Teguerichi, "with its wife and son in a cave located at Osérare. As time passed the Rarámuris [another name for Tarahumara] grew tired of him because each fertility period and crop time, this giant misbehaved and stole their food and women. So they decided to invite him to drink tesvino to get him drunk and then posion him with chilicote (a red colored bean that grows wild in the hills of Chihuahua).". 
Other creatures lived in the upper parts of the hills (Alta Tarahumara), like Bichiguare at Narárachi, set at an altitude of 2,290 m (7,500 ft). A very tall Tarahumara lived there, who had the same features of the "uribi" who also appeared during the crop period and also misbehaved. So he too was invited to a feast and they gave him chilicote. After that they burned him in his cave. 
The fact that they called him a "very tall Tarahumara" means that he was probably a giant-human (or should I say Neanderthal-human) hybrid.
Notice how all stories agree upon the "poisoning" part. These were giants that had to be exterminated. They probably competed with humans for the best crop land or for scarce natural resources during droughts. They were enemies.
Holguín says (adopting a more mainstream science approach) that thse giants are the memories of inter-ethnic strife between Tarahumara and Tubares, who were "characterized by being of a greater height than the other natives... some skeletons measure over 2 m tall" (6 ft. 7"). 
Lumhotz described the Tubares as enemies of the Tarahumara: "They are said to have been fierce and constantly fighting the Tarahumares..." , I did not find any reference to them being tall, however Holguín says that they were "very tall". 
Finally, Holguín adds that the Tarahumara were not alone in their beliefs about giants, the Acaxeess or Chichimecas, Chinipas, Pima and Guarojíos also believed in giants. Which she attributes to the fossil remains of prehistoric animals.
The following image  from the The John Lenk Collection, Tarahumara / Raramuri, Wooden Mask with White Fur Beard collected in Copper Canyon area in Chihuahua around 1965. It has a striking "hominin" appearance. The source of the image describes it as: "Copper Canyon, Chihuahua Mexico – Primitive male mask with applied fur for beard, mustache, brows, and sideburns. Roughly carved unfinished blonde wood with open mouth, peg teeth, and fearsome expression reminiscent of a Yeti or Bigfoot. Beard is white fur, possibly goat skin. Brown hair used in other areas is softer, possibly coyote or dog. Fur is still attached to tanned hide, and is delicate from age. Lots of character.". 
To close today's post, I include the following link Chihuahua mine ghost, which links to a blog post about a creature living in a mine in Chihuahua (the territory of the Tarahumara), which was reported in a newspaper back in 1892. The beast was described as: "resemble[s] a huge ape with hairy body and long, powerful arms. It is misshapen, and with deep sunken eyes...". There is even a drawing of it, representing it as a gorilla-like beast.
By the way, there are several myths (I googled them in Spanish under "fantasma mina Chihuahua" and came across several reports)on ghosts in mines in Chihuahua. Perhaps they reflect the ancient myths of primitive gigantic "cavemen" who succumbed to the encroaching Homo sapiens.
 David Roberts, In the land of the Long-distance runners, Mexico's copper canyon is home to the great athletes, the Tarahumara. Smithsonian, May 1998, V.29:2 - 43-52
 Carl Lumholtz, (1902). Unknown Mexico; a record of five years' exploration among the tribes of the western Sierra Madre. New York, C. Scribner's sons. pp. 299.
 Guadalupe Holguín, (2011). Asolan a rarámuris los “gigantes o ganokos”. El Observador. Chihuahua, Chih. 28 March 2011.
 The John Lenk Collection. Tarahumara / Raramuri Wooden Mask with White Fur Beard
Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia Copyright 2009-2014 by Austin Whittall ©