Mills first gained public attention in 1959 when, at the age of 12, she made film debut in Tiger Bay. She won a Juvenile Academy Award for her performance in Pollyana. Her other film credits include the hit The Parent Trap, Whistle Down the Wind, In Search of the Castaways, That Darn Cat!, The Chalk Garden, The Family Way, Pretty Polly, Twisted Nerve, Mr. Forbush and the Penguins, Endless Night, Deadly Strangers and The Kingfisher Caper. She made her stage debut in London in 1969 in the title role of Peter Pan and went on to appear in numerous West End productions. In 1991 in Australia, she starred as Anna in The King & I. When a U.S. national tour of the musical was launched in 1997, she reprised her performance. She made her New York stage debut in Noel Coward's A Suite in 2 Keys, for which she won a Theatre World Award. More recently, she appeared Off-Broadway in the long-running hit The Vagina Monologues.
The recent Broadway revival of On Golden Pond starred James Earl Jones as Norman Thayer Jr. and Leslie Uggams as Ethel Thayer. Jones received a Tony nomination for his performance and the show itself was nominated for Best Revival. On Golden Pond ended its Broadway production on June 26 after 19 previews and 93 regular performances at the Cort Theatre.