No, Hatchet is not a true story. The movie is based on a horror novel of the same name, written by author Victor Salva. The novel centers around a group of tourists trapped in the Louisiana Bayou with a deformed, murderous monster that haunts them. While the novel itself is fiction, parts of the movie relate to real events that occurred in New Orleans during the late 19th and early 20th centuries.
Hatchet portrays the story of a tourist, Ben, and his vacation in the Louisiana Bayou. After being dropped off by an air boat, he finds himself in a secluded swamp, where he encounters a deformed monster. This monster, known as "Victor Crowley," is based on a real serial killer nicknamed "The Axeman of New Orleans," who was responsible for a series of mysterious unsolved murders between 1918 and 1919.
In addition, the movie was partially inspired by a real location in the Louisiana Bayou, which features in the novel and the movie. This location, Honey Island Swamp, is known for its dark and mysterious atmosphere, and is home to an array of native wildlife, as well as rumored cryptozoological creatures such as the Rougarou.
In summary, Hatchet is not a true story, but rather a fictitious horror novel written by Victor Salva, with elements loosely based on real events such as The Axeman of New Orleans and Honey Island Swamp in the Louisiana Bayou.