Entering Syracuse University in 1947 on swimming and painting scholarships, Taylor began dance training in 1951. He subsequently studied modern dance with Martha Graham, Doris Humphrey, and José Limón and ballet with Antony Tudor and Margaret Craske. He began his professional career in 1953 with Martha Graham's company, creating such important roles as Aegisthus in Clytemnestra (1958), Hercules in Alcestis (1960), and Theseus in Phaedra (1962). He also performed in works by other modern choreographers, including those of Charles Weidman and Merce Cunningham. He danced a solo created for him by George Balanchine in Episodes (1959), a work choreographed by Balanchine and Graham to music by Anton Webern.

As a choreographer Taylor utilized a wide variety of movement styles, some of which he described as “flat” (two-dimensional in appearance), “dance scribbling” (emphasis on action rather than on shape or line), and “lyric” (“long arms”). His avant-garde works range from Duet (1957), in which he and his partner remained motionless for four minutes, to Orbs (1966), an hour-long composition to Beethoven's last string quartets. Other well-known dances include Three Epitaphs (1956), Aureole (1962), Scudorama (1963), The Book of Beasts (1971), Esplanade and Runes (1975), Cloven Kingdom (1976), Aphrodisiamania (1977), Airs (1978), Nightshade (1979), and Le Sacre du Printemps (1980). His Aureole entered the repertoires of such major ballet troupes as the Paris Opéra Ballet and the Royal Danish Ballet.

Taylor's company, established in 1954 and usually numbering 13 dancers, first performed in Europe in 1960, toured South America in 1965 under the International Cultural Exchange Program of the U.S. State Department, and in 1978 toured the U.S.S.R. and appeared on the U.S. public-television network. Taylor also choreographed for the Spoleto (Italy) Festival of Two Worlds and won several prestigious awards. He withdrew from performing in the 1970s.