Mudd was born in Washington, D.C. His father, John Kostka Dominic Mudd, was the son of a tobacco farmer and worked as a map maker for the United States Geological Survey; his mother, Irma Iris Harrison, was the daughter of a farmer and a lieutenant for the United States Army Nurse Corps and then a nurse at the physiotherapy ward in the Walter Reed Hospital, where she met Roger's father. Roger attended DC Public Schools and graduated from Wilson High School in 1945.