Schumann made her debut in Germany at the Hamburg Opera in 1910 and stayed with the company until 1919. She made her New York debut at the Metropolitan Opera in 1914 with the part of Sophie in Richard Strauss's Der Rosenkavalier. At Strauss's urging Schumann joined the Vienna Opera in 1919, remaining until 1938, when the Nazi takeover of Austria prompted her to leave the country. She toured the United States with Strauss in 1921, giving concerts with the composer as her accompanist. She gave an acclaimed performance in the role of Sophie for her London debut at Covent Garden in 1924. Sophie remains the role most associated with Schumann, but Schumann's high soprano voice and pure tone also helped her excel at Mozartean roles and in the lieder of Franz Schubert (Schubert, Franz).

Schumann settled in the United States, taught at the Curtis Institute at Philadelphia, and in 1944 became a U.S. citizen. She was for a time married to the conductor Karl Alwin. In 1948 her work German Song was published in London.