Koppe completed an apprenticeship as a bricklayer and went to the Royal Saxon School of Construction in Leipzig. He went to Karlsruhe, Germany to work in Hermann Billing's architectural office. He attended courses at the Academy of Fine Arts and the Technical University in Karlsruhe. During this time Koppe came into contact with Max Taut. He then decided to continue his studies at the University of Munich (1908/09). In 1910 he returned to Leipzig, registered as an architect and worked in this profession until his death.
He was involved in various building projects. His work includes industrial buildings, small flats and housing estate construction. Most of his buildings still exist and are concentrated in Leipzig, but his buildings can also be found in the surrounding areas of Leipzig. During and after the First World War, his work included so-called warriors' homes (Kriegerheimstätten), designed for people from the military.
In the late 1920s, he took up styles of modern architecture. At the same time, however, he also built in various other styles, primarily those that are generally called traditionalist (in Leipzig the colony "Am Eutritzscher Park" or several buildings in the Leipzig-Marienbrunn). In Leipzig, his most famous work in the field of modern architecture includes almost a quarter of apartment buildings of the hosuing estate Krochsiedlung, the Leipzig Tennis Club and the housing estate Steinstraße. His own residential building stands not far from the Krochsiedlung at Oldenburger Str. 8
In 2005 and 2006, more than 5,000 building drawings and some business documents from Koppe were found in an unrenovated factory building in Leipzig-Großzschocher and in a cellar in Leipzig-Abtnaundorf. They were often in poor condition and are now stored in the Leipzig City Archives (Stadtarchiv Leipzig). This is interesting because documents of private architects have hardly survived in Leipzig. And certainly not to this extent.