In the early 1870s, Mundt began training as an artist - first two months with the painter Jørgen Roed and afterwards at Vilhelm Kyhn's drawing school for women, where she met her life companion the painter Marie Luplau. In 1874, both women applied to be admitted to the Academy of Fine Arts in Copenhagen, but they were both rejected - women were not admitted to the Academy of Fine Arts until 1888 with the establishment of the Academy of Fine Arts' School of Art for Women (Kunstakademiets Kunstskole for Kvinder). Because of the rejection, the two women traveled, on the advice of the painter Elisabeth Jerichau Baumann, to Munich to further their education, and where women, unlike in Denmark, had the opportunity to draw after nude model. In 1878, Mundt made her debut at Charlottenborg. In 1882–84, Mundt and Luplau went to Paris to study at the private French art academy, the Académie Colarossi, where among many others also Paul Gauguin and Helene Schjerfbeck have been studying.

After returning from Munich, Mundt established and ran, together with Luplau, until 1912 a private drawing and painting school for women, which had the right to graduate from the Academy of Fine Arts' Art School for Women, and they thus came to impress an entire generation of young female artists.