She was the daughter of businessman Hans Peter Friedrich Tesdorpf and Antoinette Karoline Mohrmann (formerly Abendroth).

Her teachers were Mohrhagen Bernhard and Johann Theobald Riefesell who primarily taught drawing to women of the Hamburg high society.

At the suggestion of Justus Brinckmann and Alfred Lichtwark, Tesdorpf drew a documentation of the old Hamburg cityscape during the demolition phase in the 1880s and 1890s.

In her paintings she captured everything from the mundane scenes of Hamburg, its streets, the old parts of the town and the new, the city harbor and the canals that ran through it.

Tesdorpf considered it her "mission" to capture the "old Hamburg" in images - often structures destined for demolition in the years of urban renewal.