Mora was born in Paris, to a Lithuanian Jewish father, Leon Zelik, and a Romanian Jewish mother, Celia 'Suzanne' Gelbein. She was arrested in 1942 during the Vel' d'Hiv Roundup (Rafle du Vel' d'Hiv). Her father, Leon, managed to arrange for her release from the concentration camp at Pithiviers (Loiret) before Mora and her mother, Celia, were scheduled to be deported to Auschwitz. The family evaded arrest and deportation from 1942 to 1945 by hiding in the forests of France. After the war, Mora met a wartime resistance fighter Georges Mora in Paris at the age of 17. They married in 1947. In an interview in 2004, Mora said:
"I really wanted to make love to him, because I was very humiliated that he didn't because I was 17, and he said, "I know that you are not happy but we have to wait till we get married." "Ah! Married?" So I agreed to get married to lose my virginity. That's true."
Having survived the Holocaust, Mora and her husband migrated to Australia in 1951 and settled in Melbourne, where they quickly became key figures on the Melbourne cultural scene. Georges became an influential art dealer, and in 1967 he founded one of the first commercial art galleries in Melbourne, the Tolarno Galleries.
The Mora family also owned and operated three of Melbourne's most famous cafés. The Mirka Café was opened in December 1954 at 183 Exhibition Street and was the venue for the first major solo exhibition by Joy Hester. It was followed by the Café Balzac at 62 Wellington Parade, East Melbourne and then by the Tolarno in Fitzroy Street in St Kilda, which opened in 1966. All three were focal points for Melbourne's bohemian subculture. As Mora's son Philippe recalls, "my parents literally fed artists at our home and in our restaurants". In a 2004 interview Mora stated:
Actually, the Mirka Cafe got too big, because too many people came and couldn't get in. And so we opened the Balzac Restaurant and the Balzac Restaurant was really the toast of Melbourne. It was a beautiful restaurant. But it was my husband's work of art and I only came in the restaurant to help when my husband went overseas. My husband always tried to find a big house so I could have a big studio. So one day my husband came and said, "I have bought a hotel." I did get a big studio for one week, then I had to give it to my husband for his gallery. (Laughs) And then I went on the first floor, where I had the bridal room, which was a beautiful studio.
The Mora family's social circle included many Australian artists who subsequently became world-famous: Ian Sime, Charles Blackman and Barbara Blackman, Fred Williams, John Perceval and Mary Perceval, Albert Tucker, Barrett Reid, Laurence Hope, Arthur Boyd, Sidney Nolan and Joy Hester. The Mora family were especially close friends with renowned art patrons John and Sunday Reed, and spent many weekends at their famous home and artists' colony "Heide" (now the Heide Museum of Modern Art) in the Melbourne suburb of Bulleen, and at the Reeds' beach house in Aspendale.
Mora has three children, actor Tiriel Mora, film director Philippe Mora and art dealer William Mora. They had what Philippe describes as "a culturally privileged childhood". After extramarital relationships on both sides, Mora eventually separated from her husband Georges.
Mora uses a wide range of media and her work features strongly in the permanent collection of the Heide Museum of Modern Art in Melbourne. She is a noted colourist and symbolist. Her paintings are often bright and bold, drawing heavily on a stable of recurring motifs - innocent, wide-eyed children, angels, dogs, cats, snakes and birds. For many years she has conducted workshops in painting, soft sculpture and mosaics, where countless Australians have learned from her unique approach to teaching art. In 2002 Mora was made an Officier de l'Ordre des Arts et des Lettres by the French Minister of Culture and Communication.
Mora continues to live and work in a studio in Melbourne.
Mora collaborated with Australian fashion company Gorman to launch a 23 piece collection based on four artworks.
Her murals survive on the walls of the Tolarno restaurant and gallery she previously owned in St Kilda. In 2016, a Melbourne bar-owner uncovered a lost mural on the wall of his bar, previously the Café Balzac in East Melbourne.