Schmidt began studying Mathematics in 1957 at Göttingen University. His academic teachers were in particular Kurt Reidemeister, Wilhelm Klingenberg and Karl Stein. In 1960 he transferred to Ludwig-Maximilians-Universität München where he studied functions of several complex variables with Karl Stein. Schmidt wrote a thesis on analytic continuation of such functions.
In 1962 Schmidt began work at TU München with students of Robert Sauer, in the beginning in labs and tutorials, later in mentoring and administration. Schmidt's interests turned toward programming when he collaborated with Hans Langmaack on rewriting and the braid group in 1969. Friedrich L. Bauer and Klaus Samelson were establishing software engineering at the university and Schmidt joined their group in 1974. In 1977 he submitted his Habilitation "Programs as partial graphs".
He became a professor in 1980. Shortly after that, he was appointed to hold the chair of the late Klaus Samelson for one and a half years. From 1988 until his retirement in 2004, he held a professorship at the Faculty for Computer Science of the Universität der Bundeswehr München. He was a classroom instructor for beginners courses as well as special courses in mathematical logic, semantics of programming languages, construction of compilers, and algorithmic languages. Working with Thomas Strohlein, he authored a textbook on relations and graphs, published in German in 1989 and English in 1993 and again in 2012.
In 2001 he became involved in a large project (17 nations) with the European Cooperation in Science and Technology: Schmidt was chairman of project COST 274 TARSKI (Theory and Application of Relational Structures as Knowledge Instruments).
The calculus of relations had a relatively low profile among mathematical topics in the twentieth century, but Schmidt and others have raised that profile. The partial order of binary relations can be organized by grouping through closure. In 2018 Schmidt and Michael Winter published Relational Topology which reviews classical mathematical structures, such as binary operations and topological space, through the lens of calculus of relations.
Gunther Schmidt is mainly known for his work on Relational Mathematics; he was co-founder of the RAMiCS conference series in 1994.
His textbooks on calculus of relations exhibit applications and potential of algebraic logic.