She began her career during the mid-1940s, appearing in theatre in New York City, where, shortly thereafter, she would become one of the first members admitted to the newly formed Actors Studio.

She also played a number of prominent roles on various soap operas throughout her career, including Andrea Whiting on Search for Tomorrow and Gwendolyn Lord Abbott on One Life to Live.

Copeland began working in television in the early 1950s as a guest actress on such shows as Suspense and The Web and on the live telecast of O'Neill's play The Iceman Cometh in 1960.

She portrayed Andrea Whiting (Joanne's daughter, Patti's malevolent former mother in-law) on Search for Tomorrow, twin sisters Maggie and Kay Logan on Love of Life, and roles on The Edge of Night, How to Survive a Marriage, and As the World Turns.

Her other television credits include guest appearances on The Patty Duke Show, Chicago Hope, ER, All in the Family, and Naked City.

Her film credits include Middle of the Night (1959), Roseland (1977), It's My Turn (1980), A Little Sex (1982), Happy New Year (1987), The Laser Man (1988), Her Alibi (1989), Jungle 2 Jungle (1997), The Peacemaker (1997), The Object of My Affection (1998), The Adventures of Sebastian Cole (1998), The Audrey Hepburn Story (2000), The Last Request (2006), and The Private Lives of Pippa Lee (2009).