The son of missionaries, Schaffner was born in Tokyo, Japan and raised in that country. He returned to the United States and graduated from Franklin and Marshall College in Lancaster, Pennsylvania, where he was active in drama. He studied law at Columbia University in New York City but his education was interrupted by service with the United States Navy in World War II during which he served with American amphibious forces in Europe and North Africa. In the latter stages of the war he was sent to the Pacific Far East to serve with the United States Office for Strategic Services.

Returning home after the war, he found work in the television industry with March of Time and then joined the CBS network. He won directing Emmys for his work on the original 1954 CBS teleplay, Twelve Angry Men. Schaffner earned two more Emmy awards for his work on the 1955 television play, "The Caine Mutiny Court Martial for Ford Star Jubilee." He won his fourth Emmy Award for his work on the series, The Defenders.

In 1960, he directed the stage play "Advise and Consent." His first Hollywood motion picture was praised and he directed the influential hit Planet of the Apes. His next film, Patton was a major success for which he won the Academy Award for Directing and the Director's Guild of America for Outstanding Directorial Achievement in Motion Pictures. Jerry Goldsmith composed the scores for a number of his later films, including Planet of the Apes, Papillon and The Boys from Brazil.

Schaffner married Helen Jane Gilchrist in 1948. The couple had two children.

Schaffner was elected President of the Directors Guild of America in 1987.

Schaffner died in 1989 and was interred in the Westwood Village Memorial Park Cemetery in the Westwood Village area of Los Angeles, California.