Vermehren became a member of the Royal Danish Academy of Fine Arts in 1864, and began teaching there in 1865. Among his students were P. S. Krøyer (1864–1870), Kristian Zahrtmann (1864–1868), Vilhelm Hammershøi (1864–1916) and Michael Ancher (1849– 1927). As a member of the Exhibition Committee at Charlottenborg, his work was exhibited at the Nordic Exhibition in 1872, 1883 and 1888.