The son of a professor of German philology in Kiel, Kauffmann studied art history at the universities of Munich, Berlin and Kiel, where he obtained his doctorate in 1919 with a thesis on Rembrandt's art.
In 1922, he completed his Habilitationsschrift on Albrecht Dürer under Adolph Goldschmidt at the University of Berlin.
For some time, Kauffmann worked at the Gemäldegalerie Berlin under Wilhelm von Bode and in the print room at The Hague, where he was an assistant of Cornelis Hofstede de Groot.
In 1957, he moved to the Free University of Berlin, where he was appointed the first professor of art history after World War II.
In 1964, Kauffmann did some research at the Institute for Advanced Study in Princeton, New Jersey, and in 1966 he was honorary professor at Harvard University, Cambridge, Massachusetts.