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, Pulitzer Prize-winning novel.
The 1962 film starred Gregory Peck, who won the best-actor Oscar for his portrayal of Atticus Finch, the small town lawyer who defends a black man falsely accused of rape.
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 Reese Witherspoon's first film, "The Man in the Moon," which came out in 1991. It was his last film, and the family drama brought Witherspoon notice as the younger of two teenage daughters grappling with her first love.
Among his 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."
Among his other film credits: "The Rat Race" and "The Great Impostor" (both with Tony Curtis), "Come September" and "The Spiral Road" (both with Rock Hudson), "Love with the Proper Stranger" and "Baby the Rain Must Fall" (both with Steve McQueen), "Inside Daisy Clover" (Natalie Wood), "Up the Down Staircase," "The Stalking Moon," "The Pursuit of Happiness," "The Nickel Ride," "Bloodbrothers" (Richard Gere), "Same Time, Next Year" (Alan Alda and Ellen Burstyn), "Kiss Me Goodbye" and "Clara's Heart" (Whoppi Goldberg).
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 planning for the film was in its early stages. "The book does not make speeches. It is not melodramatic."
Funeral arrangements were pending, his wife said.