In 1917, Joachim Heuer began private painting lessons under Otto Friedrich W. Sebaldt, but in 1918 he was conscripted and sent to France. After returning home, he took his final exams, but was then called back into military service in Konigsbruck near Dresden. He enrolled at the Dresden Academy of Fine Arts in 1919, and until 1923 he was a master student of Oskar Kokoschka, who gave Heuer financial assistance so that he could go on a study trip to Italy. In 1925, after returning from Italy, Heuer entered the class of Otto Hettner, which was where he met his future wife, Annemarie Strauss. After finishing his studies, Heuer took a studio in a house on Antonsplatz where he worked as a freelance artist. In 1932, Heuer was a co-founder of the Dresden Secession and was appointed its secretary. He exhibited with the Secession members for the first time that same year.
The changes in cultural policy in the Third Reich meant that Heuer was unable to exhibit his works for nearly ten years after 1936. During the Second World War, he was a medical orderly in a military hospital for horses, where he made many pictures of animals. In 1944, he married the artist Annemarie Strauss. During his wartime service he was court martialled for having publicly expressed regret at the failure of the July 1944 plot against Hitler. He was, however, able to defend himself and was released to return to the front. Heuer was captured by the French and sent to an internment camp near Lake Geneva. During one of the bombing raids on Dresden in 1945, Heuer’s studio on Antonsplatz was destroyed, along with many of his works. Heuer was released in 1946. From 1948 to 1950, he worked as a lecturer in design at the College for Industrial Design at Burg Giebichenstein in Halle. From 1950 onwards he worked as a freelance artist in Dresden and began to exhibit again, though his stylistic proximity to Cubism led to him being accused of “formalism” in the GDR. After one of his paintings was removed from a joint exhibition of artists from Dresden and Stuttgart, he was prevented from participating in state exhibitions from 1977 onwards.