Two-dimensional (2D) van der Waals materials exhibit exceptional in-plane mechanical and transport properties, yet leveraging these properties in three dimensions (3D) remains a fundamental challenge. Here, we introduce a high-throughput method for the spontaneous formation of three-dimensional auto-kirigami, self-fractured and self-folded structures that evolve during indentation of thin (<
100 nm) flakes of graphite and hexagonal boron nitride. These 3D structures provide direct access to in-plane properties via out-of-plane fractured surfaces, demonstrating enhanced electrical conductance along these edges. The 3D auto-kirigami consist of 2-4 plates, or "leaflets", that form by elastic buckling facilitated by in-plane fracture. By analyzing hundreds of leaflet geometries, we demonstrate that leaflet length correlates with buckling load, enabling a real-time predictor of the leaflet morphology. These 3D auto-kirigami provide a high-yield, deformation-driven platform for 3D van der Waals structures that can leverage in-plane properties of 2D materials.