Bluiett was born just north of East St. Louis in Brooklyn, Illinois, a predominantly African-American village that had been founded as a free black refuge community in the 1830s, and which later became America's first majority-black town. As a child, he studied piano, trumpet, and clarinet, but was attracted most strongly to the baritone saxophone from the age of ten. He began his musical career by playing the clarinet for barrelhouse dances in Brooklyn, Illinois, before joining the Navy band in 1961. He attended Southern Illinois University Carbondale. In his mid-twenties, Bluiett heard Harry Carney play in a live concert in Boston, which also made a strong impression on the young Bluiett, providing an example of a baritone saxophonist who played as soloist rather than accompanist. Following his time in the Navy, he returned to the St. Louis area in the mid-1960s. In the late 1960s Bluiett co-founded the Black Artists' Group of St. Louis, Missouri, a collective dedicated to fostering creative work in theater, visual arts, dance, poetry, film, and music. He led the BAG big band during 1968 and 1969. In fall 1969, Bluiett moved to New York City, where he would join the Charles Mingus Quintet and the Sam Rivers large ensemble. In 1972, Bluiett joined Charles Mingus and toured to Europe with him. He would often play off and on with him, leaving at some points to play with another band, but would come back a year later. In 1974, Bluiett returned to Mingus and played in quintet alongside George Adams. He also performed in Mingus at Carnegie Hall. He continued to play with Mingus until 1975, when he left to make his own recordings as a leader. In 1976 he co-founded the World Saxophone Quartet along with two other Black Artists' Group members, Julius Hemphill and Oliver Lake, as well as multi-reedist David Murray. He has remained a champion of the somewhat unwieldy baritone saxophone, organizing large groups of baritone saxophones. In the 1980s, he also founded the Clarinet Family, a group of eight clarinetists playing clarinets of various sizes ranging from E-flat soprano to contrabass. Since the 1990s Bluiett led a quartet, the Bluiett Baritone Nation, made up entirely of baritone saxophones, with drum set accompaniment. Bluiett also worked with Babatunde Olatunji, Abdullah Ibrahim, Stevie Wonder, and Marvin Gaye. He returned to his hometown of Brooklyn, Illinois, in 2002 but moved back to New York City in 2012. In his final years, he performed at gigs, including the New Haven Jazz Festival on August 22, 2009. He performed with students from Neighborhood Music School in New Haven, Connecticut. The group were known as Hamiet Bluiett and the Improvisational Youth Orchestra. He died in St. Louis, Missouri on October 4, 2018 after a period of declining health.