Diamond was born in London, Ontario, Canada in 1920 to a tailor and his wife, but moved at a young age to Brooklyn, New York. She was graduated from New York University and published cartoons and humour essays in The New Yorker before moving to the West Coast, hiring an agent, and finding work in radio and, eventually, television. Her first radio writing credit was in 1943 on Pabst Blue Ribbon Time with Groucho Marx, the Camel Caravan with Jimmy Durante and Garry Moore, The Drene Show with Rudy Vallee, Duffy's Tavern, and The Kenny Baker Show. In 1950, she became one of the staffers hired by legendary comedy Writer Goodman Ace (who'd previously hired her for some work on Danny Kaye's short-lived 1940s' radio show) for The Big Show (1950–52), the ninety-minute weekly program hosted by Actress Tallulah Bankhead. Considered one of the last great variety shows of the classic old time radio era, this Sunday night comedy marathon featured some of the biggest entertainers of the era.

By the 1960s and 1970s, Diamond was familiar as a frequent guest on The Jack Paar Show and The Tonight Show Starring Johnny Carson, and she made numerous film appearances, including Stanley Kramer's comedy It's a Mad, Mad, Mad, Mad World (as the unseen telephone voice of Spencer Tracy's wife, Ginger Culpepper), Bang the Drum Slowly (as hotel switchboard operator Tootsie), and All of Me (as Margo). In 1982, she appeared in My Favorite Year with a memorable small role as wardrobe mistress for King Kaiser's Comedy Calvalcade, a fictional show which clearly echoed the time and venue of her work for Sid Caesar. She was also a semi-regular for four seasons of the Ted Knight comedy series Too Close For Comfort.

For many years, Diamond resided in a co-op apartment at 60 Sutton Place South in Manhattan until she moved out in the late 1970s. The diminutive Diamond, who was a chain smoker, was one of the original cast of Night Court until she was stricken with lung cancer and died at age 64 in Los Angeles. By tragic coincidence, her successor playing the bailiff, Florence Halop, was also lost to lung cancer after her one year in the cast of Night Court.

Diamond wasn't always taken seriously by her writing peers. Bob Schiller, who had also written for Duffy's Tavern and The Adventures of Ozzie and Harriet, told author Jordan R. Young (for The Laugh Crafters), "The jury is still out on whether Selma was a comedy Writer. She was really a very interesting character—salty, and she was—exactly what you saw on camera is what she was."