To address the structural safety of ancient masonry arch bridges under extreme flood conditions, this paper takes an ancient brick–stone arch bridge as the prototype and adopts the Coupled Eulerian–Lagrangian (CEL) method to construct a fully discrete three-dimensional refined masonry numerical model. Two parameters including cohesive surface damage (CSDMG) and contact status (CSTATUS) are introduced to analyze the flood discharge capacity, stress field evolution, and damage evolution of the bridge under different discharge conditions. The results show that when the flood discharge approaches 2030m³/s, a backwater effect occurs, adversely affecting the bridge structure. Meanwhile, due to the absence of water-deflecting stone protection, the upstream side span is prone to stress concentration, which triggers interfacial damage. When the displacement of the upstream side span exceeds 10 mm, the load-transfer path of the bridge changes, and contact failure and masonry block sliding occur at the arch springing of the second downstream span, further reducing the overall structural stability of the bridge. This study reveals the damage mechanism of ancient brick–stone arch bridges that flood impact leads to reconstruction of load-transfer paths via cohesive damage between masonry units and further induces arch springing failure, which can provide references for flood protection and reinforcement design of similar ancient masonry arch bridges.