Avalanche resistive switching is the fundamental process that triggers the sudden change of the electrical properties in solid-state devices under the action of intense electric fields. Despite its relevance for information processing, ultrafast electronics, neuromorphic devices, resistive memories and brain-inspired computation, the nature of the local stochastic fluctuations that drive the formation of metallic regions within the insulating state has remained hidden. Here, using operando X-ray nano-imaging, we have captured the origin of resistive switching in a V2O3-based device under working conditions. V2O3 is a paradigmatic Mott material, which undergoes a first-order metal-to-insulator phase transition together with a lattice transformation that breaks the threefold rotational symmetry of the rhombohedral metallic phase. We reveal a new class of volatile electronic switching triggered by nanoscale topological defects appearing in the shear-strain based order parameter that describes the insulating phase. Our results pave the way to the use of strain engineering approaches to manipulate such topological defects and achieve the full dynamical control of the electronic Mott switching. Topology-driven, reversible electronic transitions are relevant across a broad range of quantum materials, comprising transition metal oxides, chalcogenides and kagome metals.