Clinton Graydon was a native of Abbeville County. He received his education at Belmont Abbey in Charlotte, North Carolina, and at the University of South Carolina, where he received A.B. and LL.B. degrees. In 1915, he married Raven Simkins of Edgefield. His son, Augustus T. Graydon, is a member of the Columbia Bar.
He was a member of the Richland County, South Carolina and American Bar Associations. He was also a member of the American College of Trial Lawyers. He frequently served as an Acting Associate Justice for the South Carolina Supreme Court and as a Special Circuit Judge. As a trial lawyer, he was notable for the extent of his practice and the ability he displayed.
Of Clint Graydon, Judge Soper of the United States Court of Appeals said, “He had a distinction, color and imagination that set him apart from the rest.” A lover of books, he was an avid reader and an interesting conversationalist. He was a member of the Trinity Episcopal Church in Columbia.