Born Estelle Scher in New York on July 25, 1923, Getty began her career in Yiddish theater. Her most important stage role was as Mrs. Beckoff, Harvey Fierstein's mother, in both the off-Broadway and Broadway productions of Torch Song Trilogy, a role that brought her a Drama Desk Award nomination. Her website quotes a passage from her autobiography, If I Knew Then What I Know Now...So What? Contemporary Books, 1988: "I've played mothers to heroes and mothers to zeroes. I've played Irish mothers, Jewish mothers, Italian mothers, Southern mothers, mothers in plays by Neil Simon and Arthur Miller and Tennessee Williams. I've played mother to everyone but Attila the Hun."
Getty created the role of feisty, plain-spoken Sophia in The Golden Girls in 1985 and frequently stole the show from co-stars Bea Arthur who played her daughter, Dorothy, Betty White and Rue McClanahan. She received six Emmy Award nominations and won the prize in 1988. Her film roles included playing mother to Cher Mask, 1985, Barry Manilow Copacabana, 1985, and Sylvester Stallone Stop! Or My Mom Will Shoot.
Under five feet tall, Getty was said to identify with life's underdogs, having experienced discrimination against her height and age. "Being tiny has been difficult for me in a business that regarded physicality as the most important part of your life," Getty was quoted as saying on her website. "And I always had to fight against the fact that I could do things even though I was small. And eventually I proved to them I could play mother to six footers."
She was married to Arthur Gettleman from whose name she adapted her stage name from 1946 until his death in 2004 and was the mother of sons Carl and Barry.