Mark A. Saper was born in New York City, where he lived for several years. His family moved to Connecticut when his father, an electronic engineer, took a job there. His mother had a degree in accounting but stayed home with the children (Mark and his two younger brothers) while they were still young. Then she went back to school and eventually began work as a data processor at Yale University. During this his father took a job in New Jersey, so Saper had responsibilities at home in addition to his schoolwork and Hebrew school. He manifested an early interest in and talent for mathematics, but his brother surpassed him, even becoming a mathematics professor. In high school Saper became a drum major, very interested in music, joining the marching band. He also liked biology, writing an exceptional paper on protein biosynthesis. After graduation from high school Saper used his bar mitzvah money to spend seven weeks in Israel.

Looking for a school with a good marching band and music program, Saper matriculated at the University of Connecticut. His freshman advisor was a professor of biophysics who steered him into chemistry; organic chemistry sparked his interest in biology. He worked one summer at his uncle's engineering firm and a later summer in Janos Varga's laboratory. After Saper and the University marching band visited Europe during his sophomore year, Saper found that he had to give up the serious pursuit of music to focus on science. He discovered crystallography in a biophysics class and decided to go to graduate school rather than medical school. He chose Rice University, where he studied the structure of sterols in Florante Quiocho's lab. He was also very interested in computers and graphics software, which he used to trace the polypeptide chain. He went again to Israel to present two papers.

Saper spent another year in Quiocho's lab until a Weizmann fellowship came through; then he went to Rehovot, Israel. His wife-to-be found a program in Jerusalem, so they were able to see each other enough to become engaged; they then returned to Houston to be married and then went back to Israel to finish Saper's postdoc. There and in Germany he worked on ribosomal crystallography in Joel Sussman's and Ada Yonath's labs. Next Saper accepted a position in Don Wiley's lab at the Howard Hughes Medical Institute at Harvard, where he was attempting to develop software to study human leukocyte antigen (HLA), working with Pamela Bjorkman.

He accepted an assistant professorship at the University of Michigan, where he remains today, teaching; working in his lab; publishing; working on the structure of protein tyrosine phosphatases and protein secretion in Yersinia; and balancing his work with life with his wife, Cindy, and his three sons.