He was asked to organize the American Negro Dance Company to represent the United States at the First World Festival of Negro Arts in Senegal in 1966. The project fell through because of a lack of money, but in 1967 the United States Information Agency invited him to form the National Ballet Company of Brazil.
Mr. Mitchell also taught ballet at studios, including the Katherine Dunham School in New York and the Jones-Heywood School of Ballet in Washington, both important centers for black dancers. At Jones-Heywood, the dance critic Jean Battey wrote in The Washington Post, Mr. Mitchell “goes at the boys like a tough drill sergeant.”
That approach served him well in the earliest days of Dance Theater of Harlem, which started with classes in a remodeled garage and made its official debut in 1971 with a program of three ballets by Mr. Mitchell at the Guggenheim Museum.
Balanchine and Jerome Robbins contributed works to the repertoire, and later that year the company performed at the Spoleto Festival and in the Netherlands. The company had its first regular seasons in New York and London in 1974. In 1988, it visited the Soviet Union, and performances sold out in Moscow, Tblisi and Leningrad.
The troupe toured South Africa in 1992, offering its educational programs wherever it performed. As the company grew, Mr. Mitchell gave up choreography and concentrated on putting together a wide-ranging repertoire of classics and contemporary work.
Classical productions were tailored to his black dancers, with costumes designed to flatter a variety of skin tones. His restaging of “Giselle” transferred the ballet to 19th-century Louisiana, with Creole characters, and the forest setting of “Firebird” became a lush jungle.
Mr. Mitchell also revived long-ignored ballets like Fokine’s “Scheherazade” and Valerie Bettis’s “A Streetcar Named Desire,” and he encouraged black choreographers like Louis Johnson and Billy Wilson to create work for his dancers. Mr. Mitchell’s honors include the 1971 Capezio Award, the 1975 Dance Magazine Award and, in 1993, a Kennedy Center Honor and a Handel Medallion from New York City.