Born in French-speaking Switzerland, Crotti studied art in Paris and experimented with Cubism and Orphism amid the social instability that followed World War I. In 1914, he moved to New York with his first wife, Yvonne Chastel, where he met Francis Picabia and Marcel Duchamp, with whom he became close friends. In 1915, he created Portrait of Marcel Duchamp (Sculpture Made to Measure) and, in 1919, married Suzanne Duchamp.