Griffin was born July 6, 1925, in San Mateo, California, to Mervyn Edward Griffin, Sr., a stockbroker, and Rita Elizabeth Griffin (née Robinson), a homemaker. The family was Irish American. Raised as a Roman Catholic, Griffin started singing in his church choir as a boy, and by his teens was earning extra money as a church organist. His abilities as a pianist played a part in his early entry into show business.
He attended San Mateo High School, graduating in 1942, and continued to aid in financing the school. He attended San Mateo Junior College and then the University of San Francisco. He was a member of the international fraternity Tau Kappa Epsilon.
During World War II, Griffin was declared 4F after failing several military physical examinations due to having a slight heart murmur. During the Korean War several years later, he was examined and deemed healthy enough to serve, but by that time was above age 26 and therefore exempt from the draft.