Raised in Troy, New York, Stapleton moved to New York City right out of high school and began studying at Herbert Berghof Acting School. She later also trained at the Actor's Studio. She made her Broadway debut in 1946 in The Playboy of the Western World. Stapleton then appeared in three more Broadway shows Antony and Cleaopatra, Detective Story and The Bird Cage before landing her big break as Serafina Delle Rose in The Rose Tattoo. Stapleton won both a 1951 Theatre World Award and Tony Award for her performance in the drama. Over the next three decades, she would appear in over 15 more Broadway productions. She received Tony nominations for The Cold Wind and the Warm, Toys in the Attic, Plaza Suite and The Little Foxes, winning her second Tony in 1971 for Best Actress in a Play for The Gingerbread Lady.
Stapleton is survived by a son, daughter and brother.