Soil-structure interaction problems are an important issue in the research field of geotechnical engineering. Understanding and modeling the soil-structure interaction problems is thus critical. Such interaction problems involve the mechanical behaviors of both soil and structure as well as their complex interaction. Discontinuous deformation method (DDA) is appropriate for modeling mechanical behavior of structure, while smoothed particle hydrodynamics (SPH) offers a feasible technique for describing the mechanical behavior of soil material. A coupled DDA-SPH method can integrate the advantages of both DDA and SPH. For three-dimensional (3-D) dynamic analysis of the soil-structure interaction problems, the original 3-D coupled DDA-SPH method must be extended, which is the primary purpose of this paper. In the extended 3-D coupled DDA-SPH method, an elastic-plastic soil constitutive model associated with the Drucker-Prager yield criterion is implemented. The interaction between soil and structure is realized through a newly proposed coupling scheme based on a penalty method using the Mohr-Coulomb failure criterion. Furthermore, the extended 3-D coupled DDA-SPH method is validated through the investigation of four experiments. The simulation results suggest that the extended 3-D coupled DDA-SPH method can accurately simulate the large deformations and post-failure behavior of soil-structure interaction problems.