Clemmie Spangler was born in Charlotte, North Carolina. He graduated from the University of North Carolina where he was a member of Sigma Alpha Epsilon Fraternity, and received an M.B.A. from Harvard University.
He started his career by heading his father's bank, the Bank of North Carolina, merging it with NCNB in 1982. NCNB is now part of Bank of America. From 1982 to 1986 he served as chair of North Carolina's Board of Education. He then served as President of the University of North Carolina system, from 1986 to 1997.
He served as President of Harvard University's Board of Overseers from 2003 to 2004. The Spangler Center at Harvard Business School is named for him. Through his C.D. Spangler Foundation, he has donated to the University of North Carolina, Harvard University, and to Charlotte's Teach for America. As a hobby, he likes to fix old clocks.