Born Sandra Dale Dennis in Hastings, Nebraska, and a high-school classmate of Dick Cavett, Dennis made her television debut in 1956 in The Guiding Light and her film debut in Splendor in the Grass (1961). However she was more committed to following a career in the theater.

She won consecutive Tony Awards for her performances in A Thousand Clowns and Any Wednesday, and the Oscar for Best Supporting Actress for her role in Who's Afraid of Virginia Woolf? (1966). She followed this with well-received performances in Up the Down Staircase (1967), The Fox (1967), Sweet November (1968) and The Out-of-Towners (1970).

An advocate of method acting Dennis was often described as neurotic and mannered in her performances, with many critics stating her style was better suited for the stage rather than the screen. Dennis also placed a higher priority on her stage work.

Her last significant film role was in Come Back to the Five and Dime, Jimmy Dean, Jimmy Dean (1982).

She died from ovarian cancer in Westport, Connecticut, aged 54.