Mulligan died early Saturday at his home in Lyme, Conn., after a battle with heart disease, his wife, Sandy, said Monday.
Mulligan was nominated for an Oscar for "Mockingbird," the adaptation of Harper Lee's best-selling novel, a Pulitzer Prize-winning look at a child's world shaken by the racism of a Southern town.
The story unfolds largely from the point of view of Atticus' young daughter, Scout, memorably played by Mary Badham. Phillip Alford played his son, Jem.
The New York Times wrote that in the film's opening segment "achieves a bewitching indication of the excitement and thrill of being a child."
Mulligan was also known as the director of Witherspoon's first film, "The Man in the Moon." The 1991 family drama, Mulligan's last movie, brought Witherspoon notice as the younger of two teenage daughters grappling with her first love in 1950s Louisiana.
Mulligan cast Witherspoon, a Tennessee schoolgirl at the time, after seeing her during a 10-state casting search. She was 14, already getting modeling work in Nashville, when she tried out for what she thought would be a possible job as an extra in the film, she told the publication Nashville Business and Lifestyle in 1992.
"They were real nonchalant about how I was doing," she said. "They did say that I took direction really well, and that was pretty much it." She was mailed a copy of the script a month later and got the part. During filming, she recalled, Mulligan was "real set in his ways. He was more old-school."
Among Mulligan's other credits were "Fear Strikes Out," the 1957 drama starring Anthony Perkins as troubled ballplayer Jim Piersall; "Summer of '42," the 1971 wartime coming-of-age story starring Gary Grimes and Jennifer O'Neill; and the 1972 horror hit "The Other."
He also carved out a solid career as a TV director before moving over to film, working on such drama series as "The Philco Television Playhouse" and "The Alcoa Hour."
But "Mockingbird" would remain his most famous work. In 2003, an American Film Institute listing of the top heroes in film history ranked Peck's Atticus Finch as No. 1.
"The big danger in making a movie of 'To Kill a Mockingbird' is in thinking of this as a chance to jump on the segregation-integration soapbox," Mulligan told The New York Times in 1961, while the film was still in early planning stages. "The book does not make speeches. It is not melodramatic."
Funeral arrangements were pending, his wife said.