Reliable simulation of bond behavior between stone façade panels and concrete substrates is crucial for safe façade design, particularly with mechanical anchorage. Conventional finite element models relying on tie constraints overestimate interface strength, especially in the absence of surface preparation or bonding agents. This study develops and validates a physically motivated, element deletion–based finite element methodology to accurately simulate crack initiation, propagation, and failure at the mortar–stone interface. The three-dimensional numerical models, implemented in ABAQUS and benchmarked against laboratory splitting shear tests, represent the composite system comprising a concrete substrate, sand-cement adhesive mortar, and a Travertine stone façade. Both unanchored and Z-type mechanically anchored configurations were examined. Results demonstrate the approach yields accurate predictions of failure loads and damage evolution: for unanchored specimens, the maximum numerical–experimental deviation was below 2%, while Z-type clip anchorage significantly enhanced the load-bearing capacity and altered the fracture mechanism. Compared to conventional tie or interface-layer models, the element deletion strategy provides a computationally efficient and transparent tool for capturing the failure behavior of stone–mortar–concrete composites. The findings offer insights for optimizing façade anchorage design and provide a validated numerical framework for future research.