Schorm was born into a peasant family, and spent his childhood at the family farm in Elbančice near Mladá Vožice. After communistsconfiscated the family property, he was expelled from school and moved to Zličín near Prague, together with his parents. Schorm had to become a construction worker, but in 1956 he was finally accepted at FAMU, the Film and TV School of The Academy of Performing Arts in Prague. He graduated in Film direction in 1963, together with other future members of the Czech New Wave. He began his career at the Studio dokumentárního filmu (Studio of the Documentary Film) together with cameraman Jan Špáta. Together they created many short films and documentaries of strong humanistic and emotional content, in close and longlasting collaboration. In 1964, Schorm directed his first full-length film, Každý den odvahu (Courage for Everyday) which dealt with the dillusionment of individuals victimized in the name of false ideals. He explored the ethical principles of human behavior in films such as the psychological drama Návrat ztraceného syna (Return of the Prodigal Son - 1966). He also acted minor roles in films made by his friends.

During 1970s and 1980s he was regarded as too "politically undesirable" to be involved in Czech filmmaking, and therefore concentrated more on stage direction. He was involved with many Prague companies, such as Činoherní klub, Studio Ypsilon, Theatre on the Balustrade, Semafor, Laterna Magika, and the National Theatre as well as with theatres inBrno, Olomouc, Cheb and Gottwaldov. Schorm was also a notable opera director, and directed opera performances in Prague (Fidelio in Smetana Theatre), Geneva and Stuttgart. From 1982 he was engaged by the Prague theatre Laterna Magika.

From 1964 to 1970 he taught at the Film and Television School of The Academy of Performing Arts in Prague. In 1988, shortly before his death, he created his last film Vlastně se nic nestalo. In 1992 he was posthumously awarded the Order of Tomáš Garrigue Masaryk.