The son of a doctor, Karsch was educated at the Friedrich Wilhelm University in Berlin and published a thesis on the gall wasp in 1877. From 1878 to 1921 he held the post of curator at the Museum für Naturkunde Berlin. Between 1873 and 1893, he published a catalogue of the spiders of Westphalia: he also published numerous articles on the specimens that the museum received from various explorers and naturalists working in Africa, in China, in Japan, in Australia, etc. This publication of others' work sometimes led to disputes over priority and nomenclature, for example with Pickard-Cambridge..
Alongside his zoological activities, he published many works on sexuality and, in particular, homosexuality in both the animal kingdom and in so-called "primitive" peoples, including Das Leben der gleichgeschlechtliche Kulturvölker - Ostasiaten: Chinesen, Japanese, Korea in 1906 on homosexuality in Eastern societies and in 1911 Das Leben der gleichgeschlechtliche Naturvölker. Karsch lived in later life open homosexual in Berlin. The rise of Hitler to power and Nazi repression of homosexuality led to the eclipse of his reputation.