The fate of topological transport in the strongly correlated regime raises fundamental questions on the role of geometry in quantum many-body physics. Recently, different platforms have emerged as possible probes for many-body transport beyond the traditional Hall response; these include ultracold quantum gases, Rydberg atoms, and photonics. A paradigm of quantised transport is the topological Thouless pump, which represents the one-dimensional, dynamic analogue of the quantum Hall effect. A few experiments have explored the effects of interactions on Thouless pumping in two-body and optical mean-field systems, but the strongly correlated regime has so far remained out of reach. Here, we experimentally detect the breakdown of topological transport due to strong Hubbard interactions in a fermionic Thouless pump, facilitated by a dynamical optical superlattice. We observe the deviation from quantised pumping for repulsive Hubbard $U$, which we attribute to pinned atoms in a Mott insulator. On the attractive side another mechanism is reducing the pumping efficiency: a smaller energy gap for pair pumping makes the evolution less adiabatic. The dynamical superlattice operated at a single frequency establishes a novel platform for studying topology in the presence of strong correlations in one, two, and possibly three dimensions, including avenues to fractional transport.