Slayton Alvin Evans Jr. was born on May 17, 1943, in Chicago, Illinois, to Corine M. Thompson Evans and Slayton A. Evans, Sr. Months later, his father was called to serve in World War II. When Slayton was three years old, the family moved to Meridian, Mississippi, where they lived in a segregated public housing project and his father worked at a J. C. Penney store. Slaytons interest in chemistry began early, when he was given a chemistry set. In addition, a small microscope allowed him to study various plant specimens and insects. Evans and his two younger siblings enrolled at a segregated primary school run by the Roman Catholic Church, and later he attended St. Josephs High School. In 1957, when Evans was in the ninth grade, news of the artificial satellite Sputnik inspired him to learn about rocketry and attempt to build his own. While he was given permission by the nuns at his school to buy chemicals to make rocket fuel, he had to make his own powdered charcoal. He built six rockets, two of them achieving liftoff.
Evans helped pay for his school tuition by mowing lawns and during eighth grade he was a junior assistant janitor at his elementary school. Later he worked in the high school cafeteria. In his third year of high school, he considered going into the Air Force, but was too tall for flight training. However, he took several competitive examinations and was the recipient of an academic scholarship to Tougaloo College where he also received an athletic scholarship for basketball.  He enrolled at Tougaloo in 1961.
By the end of his first year, Evans had top marks in chemistry in his class. He got a summer job working for the pharmaceutical company Abbott Laboratories in Chicago where he was tasked first with creating chemical compounds from raw materials, and later with identifying the stages of chemical reactions. Evans graduated from Tougaloo with a Bachelor of Science in chemistry in 1965. Evans was encouraged to attend graduate school, though he didnt know how to pay for it. He briefly attended the Illinois Institute of Technology before transferring to Case Western Reserve University in Cleveland, Ohio, where he was offered a research assistant position in the chemistry department. In his first year, he received a draft notice to go to the Vietnam War. University officials contacted the draft board and explained that Evans research was crucial to the war effort. He was researching a medicine to treat schistosomiasis, a disease caused by parasitic flatworms that are common in Southeast Asia. He completed his coursework in 1969 and received his Ph.D. in chemistry in early 1970.