She first came to attention with a highly-praised turn as a pre-teen murder witness in "Tiger Bay" (1959), opposite her father. Based on this strong debut, Walt Disney signed Mills to a five-year contract, putting her in a series of sweet, ingratiating innocents ranging from "Pollyanna" (1960), for which she earned a special juvenile Academy Award to a dual role of twins trying to reunite their divorced parents in "The Parent Trap" (1961). She also co-starred as one of three children who discover an escaped convict and believe he is Jesus Christ in Bryan Forbes' "Whistle Down the Wind" (1961), adapted from a novel by her mother. After playing a perturbing student at a convent school who reforms in "The Trouble With Angels" (1966), directed by Ida Lupino, Mills shocked the Establishment and shed her pure image with a celebrated nude scene in "The Family Way" (also 1966). That she also married a man three-decades her senior, producer-director Roy Boulting, changed the direction of her career.
By the early 70s, her film career was petering out, but she found renewed success as a stage actress, appearing in the title role of "Peter Pan" (1969-70) and Chekhov's "Three Sisters" (1970). After giving birth to her first child, she returned to the stage in "A Touch of Spring" (1975-76), which introduced her to Leigh Lawson, with whom she had a romantic relationship and a second son. For much of the next two decades, Mills concentrated on stage work winning praise for her work in "Talley's Folly" (1982) and "Toys in the Attic" (1985). She continued to make appearances in small screen productions, notably as the wife and mother of a family growing coffee in Kenya in the acclaimed BBC miniseries "The Flame Trees of Thika" (shown in the USA on PBS' "Masterpiece Theatre" in 1982) as well as guest appearances on such fodder as "The Love Boat" and "Murder, She Wrote". The 90s brought her to Australia, first as Anna in a restaging of the Rodgers and Hammerstein musical "The King and I" (1991) and then opposite her older sister Juliet in a production of Noel Coward's "Fallen Angels" (1992). More recently, Mills traveled across North America headlining a national tour of "The King and I".