Mr. Mitchell, who described himself as the Jackie Robinson of the ballet world, was hired by choreographer George Balanchine in 1955 to perform with the New York City Ballet and won over audiences and critics with his technical brilliance and charisma. Still, in an era when segregation was just beginning to crumble, his ascent to the upper echelon of dance met with many obstacles, from instructors who encouraged him to abandon ballet and take up other dance genres to shocked theatergoers who wrote letters expressing outrage about Mr. Mitchell being paired onstage with a white woman.