According to Matthew Cole, SEAL Team Six's Red Squadron did indeed use tomahawks:
The SEALs’ successes throughout 2002 resulted in the Joint Special Operations Command choosing the unit to lead the hunt for al Qaeda, as well as the invasion of Baghdad in March 2003. The rise of JSOC as the sharp tip of America’s military effort led to a similar increase in size and responsibility for SEAL Team 6 in the early years of America’s two post-9/11 wars. By 2006, the command rapidly expanded, growing from 200 to 300 operators. What were originally known as assault teams now formally became squadrons, and by 2008, the expansion led to the creation of Silver, a fourth assault squadron. One result of the growth was that back in Virginia, the captain in command of the entire 300-SEAL force had far less oversight over tactical battlefield decisions. It was at this point that some critics in the military complained that SEAL Team 6 — with their full beards and arms, legs, and torsos covered in tattoos — looked like members of a biker gang. Questions about battlefield atrocities persisted, though some excused these actions in the name of psychological warfare against the enemy.
Against this backdrop, in 2006, Hugh Wyman Howard III, a descendant of an admiral and himself a Naval Academy graduate, took command of Red Squadron and its roughly 50 operators. Howard, who has since risen through the ranks and is currently a rear admiral, was twice rejected by his superiors for advanced SEAL Team 6 training. But in 1998, after intervention by a senior officer at Dam Neck, Howard was given a slot on Green Team. Because of Howard’s pedigree, SEAL Team 6 leaders running the training program felt pressure to pass him. After being shepherded through the nine-month training, he entered Red Squadron. Howard took the unit’s identity seriously, and after 9/11, despite the questionable circumstances that led to his ascent, his influence steadily grew.
In keeping with Red Squadron’s appropriation of Native American culture, Howard came up with the idea to bestow 14-inch hatchets on each SEAL who had a year of service in the squadron. The hatchets, paid for by private donations Howard solicited, were custom-made by Daniel Winkler, a highly regarded knife maker in North Carolina who designed several of the period tomahawks and knives used in the movie “The Last of the Mohicans.” Winkler sells similar hatchets for $600 each. The hatchets Howard obtained were stamped with a Native American warrior in a headdress and crossed tomahawks.
At first the hatchets appeared to be merely symbolic, because such heavy, awkward weapons had no place in the gear of a special operator. “There’s no military purpose for it,” a former Red Squadron operator told me. “But they are a great way of being part of a team. It was given as an honor, one more step to strive for, another sign that you’re doing a good job.”
For some of Howard’s men, however, the hatchets soon became more than symbolic as they were used at times to hack dead fighters in Iraq and Afghanistan. Others used them to break doorknobs on raids or kill militants in hand-to-hand combat.
During the first deployments in both Iraq and Afghanistan, it was common practice to take fingers, scalp, or skin from slain enemy combatants for identification purposes. One former SEAL Team 6 leader told me that he feared the practice would lead to members of the unit using the DNA samples as an excuse to mutilate and desecrate the dead. By 2007, when Howard and Red Squadron showed up with their hatchets in Iraq, internal reports of operators using the weapons to hack dead and dying militants were provided to both the commanding officer of SEAL Team 6 at that time, Capt. Scott Moore, and his deputy, Capt. Tim Szymanski.
Howard, who declined to answer questions from The Intercept, rallied his SEALs and others before missions and deployments by telling them to “bloody the hatchet.” One SEAL I spoke with said that Howard’s words were meant to be inspirational, like those of a coach, and were not an order to use the hatchets to commit war crimes. Others were much more critical. Howard was often heard asking his operators whether they’d gotten “blood on your hatchet” when they returned from a deployment. Howard’s distribution of the hatchets worried several senior SEAL Team 6 members and some CIA paramilitary officers who worked with his squadron.
Source: Matthew Cole, The Crimes of SEAL Team 6, The Intercept, January 10, 2017.
Bold is mine.