Max Oppenheimer was born in Vienna as the older of two sons of Ludwig Oppenheimer (1828-1903), co-founder of the journalists‘ and writers’ association Concordia, and his wife Regina (neé Knina, 1851-1921). He was a student at the Academy of Fine Arts in Vienna, the Academy of Fine Arts in Prague and an important representative of Austrian Expressionism. Born into a Jewish family, the artist left the Jewish community at a young age and remained unmarried and childless. Mopp - his artist's name - lived and worked alternately in Vienna, Zurich and, until 1933, in Berlin. In autumn 1933, he moved into an apartment and studio at Neulinggasse 39 in Vienna’s 3rd district. Oppenheimer also used an atelier in the Neue Burg, where he created one of his most famous works, Die Wiener Philharmoniker (The Vienna Philharmonic).

After 1933, the Nazi regime in Germany defamed his work as ‘degenerate’ and destroyed numerous paintings. Immediately before the ‘Anschluss’ of Austria, Oppenheimer fled to Switzerland on 11 March 1938, leaving his property behind. With the help of the Zurich Art Association, he was able to bring some of his paintings from his Vienna atelier in the Neue Burg to Switzerland in April 1938. On 18 May 1938, Nazi authorities carried out investigations in his home on Neulinggasse. Most likely, the flat was subsequently cleared and the furnishings seized. Three paintings Porträt Martin Hürlimann, Selbstbildnis, Porträt Moise Kogan (Portrait of Martin Hürlimann, Self-Portrait, Portrait of Moise Kogan) created between 1929 and 1932 and shown at the autumn exhibition at the Künstlerhaus in the same year were donated to the Historical Museum of the City of Vienna (now the Wien Museum) by Julius Fargel in February 1939. Fargel worked as an appraiser for the Vermögensverkehrsstelle (Property Transaction Office), the Gestapo and the Vugesta, and as a painting restorer, he was on friendly terms with the director of the museum, Karl Wagner. After his residence permit in Switzerland expired at the end of 1938, Oppenheimer emigrated to New York with the help of art historian and philanthropist Edward Warburg in January 1939. Die Philharmoniker (The Philharmonics) was shown at the 1939/1940 World's Fair in San Francisco, and the Nierendorf Gallery organised Max Oppenheimer's first solo exhibition in the USA in 1940.

Oppenheimer became an American citizen in 1948 and changed his surname to Mopp, the wording of his painter's signature. His brother Friedrich, who had become a writer and changed his surname to Heydenau, returned to Vienna from exile in New York and remarried his wife, whom he had divorced in 1939. In 1948, the Wien Museum (Historical Museum of the City of Vienna) organised an exhibition of Viennese portraits, including Oppenheimer's self-portrait, which had been expropriated from the collection in 1939. Mopp demanded the return of his three paintings from the museum, the whereabouts of which he had not known until then. Stalled by museum director Wagner, let down by his lawyer and embittered by the way his colleagues and museum experts treated him, Mopp resigned and gave up his efforts to get his paintings back. Wagner succeeded in continuing to conceal the provenance of the paintings. Mopp died alone in his New York apartment in 1954 and is buried in Hartsdale Ferncliff Cemetery, New York.

In 2004, the Vienna Restitution Commission decided that the approximately 200 acquisitions by Julius Fargel from unknown previous owners, including the three paintings by Max Oppenheimer, should be classified as restitution-worthy and published them. In connection with the Wien Museum's new permanent exhibition, opened in 2023, and in which Mopp's self-portrait was given a prominent place, the history of the expropriation was reconstructed. In February 2024, the Viennese Restitution Commission decided to return the three once expropriated paintings to the legal successors of Max Oppenheimer. The whereabouts of countless works of art remain unknown to date, the Nazi-induced expropriation of the paintings has so far only been a marginal topic in the art-historical examination of Oppenheimer's oeuvre.