There is certainly some truth to it. The most horrific example I know of is the alleged death of Lt. Thomas Boyd during the American War of Independence.

Boyd was part of the Sullivan Expedition, one of the United States' largest military campaigns of 1779.

He was captured by the Seneca Indians. Following a bought of psychological torture:

A quote from "SULLIVAN'S CAMPAIGN AGAINST THE IROQUOIS; BEING A FULL ACCOUNT OF THAT EPOCH OF THE REVOLUTION", by A. TIFFANY NORTON

They then pulled out Boyd's nails, cut off his nose and ears, enlarged his mouth with a knife and thrust into it the severed nose, cut out his tongue, forced out one of his eyes, and stabbed him in several places. As if this were not enough they now unbound him from the tree, and making a small incision in his abdomen a severed intestine was fastened to the tree. Then by sheer brute force he was driven around the tree until his entrails were literally wound upon its trunk.

Pretty awful.

HOWEVER -- The Sullivan Expedition was a scorched-earth campaign of ethnic cleansing to punish the native allies of the British government. To quote a report attributed to Sullivan:

The number of towns destroyed by this army amounted to 40 besides scattering houses. The quantity of corn destroyed, at a moderate computation, must have amounted to 160,000 bushels, with a vast quantity of vegetables of every kind. Every creek and river has been traced, and the whole country explored in search of Indians settlements, and I am well persuaded that, except one town situated near the Allegana, about 50 miles from Chinesee there is not a single town left in the country of the Five nations. (Journals of the Military Expedition of Major General John Sullivan against the Six Nations of Indians 1779, Frederick Cook, editor, 1887, p. 303. As quoted in Founding Myths: Stories that Hide Our Patriotic Past by Ray Raphael, 2014)

This act of torture and execution was certainly not unprovoked. (Also, look at the name of that book: "Military Expedition . . . against the Six Nations of Indians 1779". Two out of those Six, the Oneida and the Tuscarora were allies of the Continental Army! Only the Seneca, Onondaga, Mohawk, and Cayuga were allies of the British government.)

The nacent United States and the Native Americans did absolutely horrible things to each other in their fights for conquest and survival, respectively.

While horrific torture and executions almost certainly occurred, one should see most accounts of them for what they are -- propaganda designed to dehumanize an enemy to make ethnic cleansing acceptable to the Anglo-American reader.

Sources: The quoted history book, in the public domain.

Wikipedia article giving context to Boyd's capture

My knowledge of the account of this execution comes from local folklore in Western New York. I had to go in search of a citation. I haven't found primary sources yet, so please take it with a grain of salt. Most of my actual knowledge of the historical context of the Sullivan Expedition comes from Founding Myths by Ray Raphael, which I just finished.