Anna Belle Sixkiller was born on October 16, 1926, near Sycamore, a small town near Jay, Oklahoma, to Oo loo tsa (ᎤᎷᏣ, Iva Louise née Owens) and Houston Sixkiller. Her family were full-blood Cherokee, who spoke the Cherokee language in their home. Her mother worked as a domestic or waitress in Jay and at night often quilted. Her father worked on their farm, raising produce to feed his family. Sixkiller began her education in the public school system in Jay. She was unable to speak English, and her teacher was indifferent. Financial struggles caused by divorce and the Great Depression led her mother to take her and her siblings out of the school. Anna and a younger sister were sent to the Seneca Indian School, one of the federally funded American Indian boarding schools, located in Wyandotte. There Anna quickly learned English but suffered from homesickness. Since the Seneca School only went to the ninth grade, after graduation, Sixkiller completed her education at the Haskell Institute, her mother's alma mater and an intertribal boarding school in Lawrence, Kansas.

Though she did not intend to become a potter, she was curious about how traditional Cherokee pottery was made and made it a personal mission to learn. She began by visiting museums in Oklahoma and Arkansas and then made trips to the Eastern Cherokee lands in North Carolina. She also made research trips to learn about pottery traditions of the Southwest Pueblo peoples and the Northeastern Woodlands people, all the while experimenting with making different pots. In 1973, Mitchell held her first public exhibition at the Tulsa Indian Trade Fair.

Mitchell's goal was to revive the art of Cherokee pottery-making for Cherokee people in Oklahoma. In 1987, Jane Osti (Cherokee Nation), a student studying at Northeastern Oklahoma State University in Tahlequah, conducted an interview with Mitchell for a heritage course. She became fascinated with the craft of pottery-making and began studying with Mitchell. Osti was later commissioned by the Cherokee Nation to create a bust of Mitchell, which was unveiled in 1990 and housed at the Bacone House on the campus of Northeastern State University. Other students who studied with Mitchell and have professional art careers her daughter, Victoria Vazquez (Cherokee Nation) and Crystal Hanna (Cherokee Nation). Mitchell also inspired Martha Berry (Cherokee Nation), encouraging her to revive the art of Cherokee beadwork. In 2008, Mitchell was honored with the Educator of Arts and Humanities Lifetime Achievement Award by the Cherokee Nation.