McClure was born in Ukiah, California, where his mother was the painter Ethel Jamison Docker. At age nine, McClure moved with his family to San Francisco, where he went to art school at night, doing his first professional jobs at age 14. He was 17 when he began an apprenticeship in animated cartoons, and he studied at the California School of Fine Arts. After work in logging camps as a lumberjack, he was a sailor on commercial freighters in the Pacific, eventually traveling to New York City on a freighter.