Born in Chicago, Illinois, Cuffey became a graduate student at Northwestern University in 1934, then went on to Harvard University as a doctoral student under Harlow Shapley.
He received his Ph.D. from Harvard in 1938, then took a position as a postdoctoral fellow at Indiana University.
Serving in the United States Navy in World War II, Cuffey taught navigation at the U.S.
In 1966, he joined Clyde Tombaugh in starting the astronomy program at New Mexico State University, where he remained until he retired in 1976.
Cuffey was married to astronomer Rita Paraboschi.