Carlson was born in Culver City, California, the son of Swedish immigrant Gustav Carlson, a machinist, and his wife Ruth. He graduated from North Park University in 1948, and went on to earn a bachelor's degree in anthropology from Stanford in 1951, and finished medical school at George Washington University in 1956. After finishing medical school, he completed five years of internship and then surgery residency in Redondo Beach, California, during which time he met and married nurse Lois Lindblom of Menominee, Michigan.
In 1961, Carlson decided to serve as a missionary doctor. He arrived in Congo and began working as a medical missionary for six months in Ubangi Province. In December 1961 he returned to Redondo Beach but continued to talk of returning to the Congo because of its great needs.
In July 1963, along with his wife, son Wayne, and daughter Lynette, he returned to the Ubangi region of the African nation known at the time as the Republic of the Congo. Activities included working in the eighty-bed hospital and leper colony. During this time, Carlson acquired the nickname Monganga Paul (Monganga meaning "doctor" in the Lingala tongue). This work continued until the political unrest of the time reached them. In August 1964, rebels captured Stanleyville, now Kisangani, and the Carlson family crossed the Ubangi river to seek refuge in the Central African Republic. Carlson, however, remained committed to his hospital and work in Wasolo, and he returned.
This final return placed him in the middle of the political unrest of the time, and he soon fell into the hands of the communist-inspired Congolese rebels of the Simba Rebellion. His home was looted, the hospital and other buildings were damaged and two of his staff members were shot. Under the unstable leadership of Christophe Gbenye, the rebels accused Carlson of being an American spy and took him as a hostage to Stanleyville. Carlson was held there and was mentally and physically tortured. In November 1964, Gbenye announced he would execute Carlson, prompting the U.S. government to begin negotiations for his release. In Stanleyville, Carlson joined the American consul as a captive of the rebels. Upon a breakdown in negotiations, paratroopers were flown in and the rebels panicked. On November 24, 1964, some Simbas soldiers opened fire into a crowd, and Carlson and several others ran to a wall in hopes of escaping. Before Carlson scaled the wall, he urged a clergyman to go first, and as he was climbing the wall after the clergyman, he was shot and killed by rebel gun fire.