Mitchell is one of four siblings and grew up in the streets of Harlem, New York. Forced to assume financial responsibility for his family in the wake of his father's incarceration, at the age of 12 Mitchell worked numerous jobs including: shoe-shining, mopping floors, newspaper delivery, and work in a meat show. Despite his duties Mitchell became involved with street gangs, though this did not ultimately deter him from finding success.
As a teenager, Mitchell was encouraged by a guidance counselor to apply for admission to the High School of Performing Arts. Upon being accepted he decided to work towards having a career in classical ballet. Following his graduation in the early 1950s, he won a dance award and scholarship to study at the School of American Ballet, the school affiliated with the New York City Ballet. In 1954, following his 1952 Broadway debut in the opera Four Saints in Three Acts, Mitchell would return to Broadway to perform in the Harold Arlen musical House of Flowers, alongside Diahann Carroll, Geoffrey Holder, Alvin Ailey, Carmen De Lavallade, and Pearl Bailey.
In 1955 Mitchell made his debut as the second African American with the New York City Ballet (NYCB), performing in Western Symphony. Rising to the position of principal dancer with the company in 1956, he performed in all the major ballets in its repertoire, including A Midsummer Night's Dream, The Nutcracker, Bugaku, Agon, and Arcade.
Mitchell was the second African-American dancer with the NY City Ballet until 1970. Choreographer and director of the NYCB George Balanchine created the pas de deux in Agon especially for Mitchell and the white, Southern ballerina Diana Adams. Audience members initially complained about partnering Mitchell with a white woman, but Balanchine refused to change the pairing. Although Mitchell danced this role with white partners throughout the world, he could not perform it on commercial television in the United States until 1968, when the performance aired on Johnny Carson's The Tonight Show.
Mitchell left the New York City Ballet in 1966 to appear in several Broadway shows, and helped found ballet companies in Spoleto, Washington, D.C. and Brazil, where he directed a dance company. The Company he founded in Brazil was the National Ballet Company of Brazil.
After the assassination of Dr. Martin Luther King, Jr. in 1968, Mitchell returned to Harlem, where he was determined to provide opportunities in dance for the children in that community. A year later, he and his teacher Karel Shook formed a classical ballet school. Mitchell had $25,000 of his own money to start the school. About a year later he received $315,000 in a matching funds grant from the Ford Foundation. Dance Theatre of Harlem (DTH) was born in 1969 with 30 kids in a church basement in a community where resources of talent and creative energy were virtually untapped. Two months later, Mitchell had attracted 400 youngsters attending classes. Two years later they presented their first productions as a professional company. Mitchell used his personal savings to convert a garage into the company's first real home.
In Harlem, DTH created an explosion of professional opportunity in dance, music, and other related theater activities. The school has an outstanding number of former students who have been successfully engaged in careers as dancers and musicians, as technicians in production, stagecraft, and wardrobe, and in instruction and arts administration. With this success, DTH challenged the classical dance world to review its stereotypes and revise its boundaries.
Mitchell's archives are to be held at Columbia University.
Mitchell has received numerous awards in recognition of his groundbreaking work and achievements, including:1993 – Kennedy Center Honors, one of the youngest persons recognized.
1994 – Named as a MacArthur Fellow.
1995 – United States National Medal of Arts, presented by the President
1999 – Inducted into the National Museum of Dance C.V. Whitney Hall of Fame, Saratoga Springs, NY.
2001 – The 7th Annual Heinz Award in the Arts and Humanities.
2005 – Awarded a Fletcher Foundation fellowship in its inaugural year, in recognition of his contributions to African-American culture.
2006 – Mitchell and the Dance Theatre of Harlem were honored at the White House by President Bush with a dinner in his honor.
In addition, Mitchell has received honorary doctorates from numerous leading universities, including Hamilton College, Brown University, City College of the City University of New York, Harvard University, The Juilliard School, The New School for Social Research, North Carolina School of the Arts and Williams College. He has also received awards from the City of New York and community organizations.