Structural failure under fluid-structure interaction (FSI) is a type of strong nonlinear problem, which involves structural motion, deformation and failure as well as complex free-surface flows. Considering the respective advantages of peridynamics (PD) and smoothed particle hydrodynamics (SPH) as well as their computational efficiency, a multi-resolution PD-SPH coupling approach suitable for solving complicated FSI-concerned structural failure problems was proposed. The fluid and solid are discretized and solved by using SPH and PD approaches with different spatial and temporal resolutions, respectively. To achieve the precise satisfaction of interface boundary conditions, the fluid-structure interface is treated by using virtual particle technology, in which the same smoothing length of virtual particles as fluid particles is adopted. The modeling and analysis for two benchmark tests: large deformation of an elastic plate with hydrostatic pressure, and dam-break flow through an elastic gate, show that the presented multi-resolution PD-SPH coupling strategy and approach is suitable for simulating fluid-structure-interaction problems with satisfactory accuracy and efficiency. Further, the process of hydraulic fracture in Koyna gravity dam with an initial crack is simulated, and the cracking path in the simulation agrees well with available literature results, which indicates that the proposed coupling approach is appropriate for solving FSI-concerned structural failure problems. Finally, the proposed coupling strategy and numerical approach is employed to investigate the collapse process of a concrete slab due to fluid flow impacting, and the whole process of the concrete slab fracture as well as the motion of the fluid are captured with high accuracy. The results show that the proposed multi-resolution PD-SPH coupling approach may provide a potential alternative to simulate the process of structural failure under fluid-structure interaction.