Born in the Duchy of Mecklenburg-Strelitz (now Germany), Mahncke, his wife, Katarina, and two daughters settled in San Antonio, Texas, in 1882. Within four years, Mahncke had purchased the Vance Hotel (renaming it the Mahncke Hotel) and become a successful businessman. In 1899 he encouraged philanthropist George W. Brackenridge, his close friend, to donate 199 acres along the San Antonio River to the city for parkland. Mahncke then developed the tract (named Brackenridge Park in 1912), initially constructing seven miles of winding, picturesque roads that converged at the river on the north side of the property. He soon added a deer preserve and a menagerie that included enclosures for buffalo, elk, and other animals.
In 1901 Mahncke was appointed the city’s first paid park commissioner (Anton Wulff had previously filled the position without pay). In 1904, he transplanted cypress trees from the Guadalupe River to be planted along the San Antonio River. Mahncke twice served as a member of the city council and he chaired the city’s parks committee. He resigned as park commissioner after a quarrel with Mayor Bryan Callaghan, Jr., who had appointed him to the position (Callaghan had reduced Mahncke’s allowance and would later block the installation of a bust of the deceased Mahncke in the city’s Main Plaza). Mahncke succumbed to pneumonia in 1906 and is buried in City Cemetery No. 6. In 1909 a bust of Mahncke, by sculptor Pompeo Coppini, was erected in Brackenridge Park. It was later moved to a 25-acre park donated by Brackenridge (in 1905) and named in Mahncke’s honor.