Costa was born in Knoxville, Tennessee, where she lived for much of her childhood. She sang Sunday school solos at the age of six. At Knoxville High School (Tennessee), she sang in the chorus. When she was in her early teens, Costa's family relocated to Los Angeles, California, where she completed high school and won a Music Sorority Award as the outstanding voice among Southern California high school seniors. Following high school, she entered the Los Angeles Conservatory of Music to study with famed maestro Gaston Usigli. Between 1948 and 1951, she appeared with Edgar Bergen and Charlie McCarthy on the Bergen radio show. She also sang with Dean Martin and Jerry Lewis in concerts at UCLA, and made numerous commercials for Lux Radio Theatre.
In 1952, after meeting people at a party with her future husband, director Frank Tashlin, she auditioned for the part of Disney's Princess Aurora. Walt Disneycalled her personally within hours of the audition to inform her that the part was hers. In 1958, Costa was called upon to substitute for Elisabeth Schwarzkopf at a gala concert in the Hollywood Bowl, conducted by Carmen Dragon. Because of her glowing reviews from that performance, she was invited to sing the lead in her first fully staged operatic production, The Bartered Bride, produced by the renowned German producer, Carl Ebert, for the Los Angeles Guild Opera. Ebert later requested that Mary appear at the Glyndebourne Festival, where she made a debut.
Costa impressed television audiences throughout her career with guest appearances on many shows, such as Bing Crosby’s Christmas Show on NBC-TV. She appeared with Bing Crosby and Sergio Franchi on The Hollywood Palace in 1970. She also appeared on Frank Sinatra’s “Woman of the Year”TIMEX Special for NBC, where she was honored, along with Juliet Prowse, Lena Horne, and Eleanor Roosevelt, as women of the year. In 1972, Sammy Davis Jr. asked Mary to appear on his first NBC Follies. Among his other guests that evening, were Mickey Rooney and Ernest Borgnine. Mary performed a blues selection with Sammy, backed up by one of her favorite performers, Charlie Parker. Her other televisionCREDITS include appearances on the Academy Awards, and the shows of Jim Nabors, Johnny Carson, Merv Griffin, Della Reese, Joey Bishop, George Burns, Don Knotts, Dinah Shore, and many others.
Jacqueline Kennedy asked her to sing at a memorial service for her husband, U.S. President John F. Kennedy, from the Los Angeles Sports Arena in 1963. She sang for the inaugural concert of the John F. Kennedy Center for the Performing Arts in 1971. In 1972, she starred in the Metro-Goldwyn-Mayer feature The Great Waltz, depicting the life of Austrian composer Johann Strauss II. Additional movieCREDITS include The Big Caper (1957) and Marry Me Again (1953).
Costa has dedicated her later years to inspiring children and teenagers, giving motivational talks at schools and colleges across the country. She is also a celebrity ambassador for Childhelp, a child abuse prevention and treatment non-profit organization. She continues to do promotional appearances for Disney, most recently for the Blu-ray release of "Sleeping Beauty" and the 50th anniversary of the film.
In 1989 she received the Lifetime Achievement Award of the Licia Albanese Puccini Foundation. In November 1999 she received the Disney Legends Award, and her handprints are now a permanent part of the Disney Legends Plaza at the entrance to Disney Studios. In 2000 she was selected as the Tennessee Woman of Distinction by the American Lung Association. And in April 2001, she was honored by the Metropolitan Opera Guild for Distinguished Verdi Performances of the 20th Century. In 2003 she was appointed by President George W. Bush to the National Council on the Arts, where she served until 2007. In December 2007, she was awarded an honorary Doctor of Fine Arts degree by Carson-Newman College in Jefferson City, Tennessee. On November 2, 2007, she was inducted into the Knoxville Opera Hall of Fame. Earlier she had launched the inaugural Knoxville Opera season in 1978 as Violetta in La Traviata.
In 2012, Costa served as the commencement speaker at Pellissippi State graduation ceremony. On November 10, 2014 she was awarded an Honorary Doctorate of Humane and Musical Letters from the College of Arts and Sciences, University of Tennessee, Knoxville. In 2014, Costa was named one of theYWCA Knoxville's Tribute to Women Honorees during the 30th anniversary celebration. On March 17, 2015 she was a recipient of Tennessee's 2015 Governor's Arts Award.