Geothermal energy is regarded as a promising and attractive alternative to traditional energy sources, with the concept of enhanced geothermal systems (EGS) enabling viable commercial development. EGS modeling requires the integration of multiscale, multiphysics processes, necessitating a comprehensive numerical model to effectively evaluate heat extraction performance. The advantages of explicitly representing fracture networks and directly simulating thermal-hydrologic-mechanical (THM) coupling processes, coupled with the trend toward increasing computational power, suggest that the discrete approach is the optimal way for modeling fractured rock mass. Consequently, the discrete fracture matrix (DFM) model has seen rapid development. In contrast, discontinuity-based formulations, such as the displacement discontinuous method (DDM), explicitly treat fractures as discontinuities and kinematically resolve their evolution in association with the rock matrix, offering greater fidelity than the static DFM models. However, to the authors' best knowledge, most DDM models tend to overlook or simplify the details of fluid-heat flow within the matrix, making them less commonly used in EGS where fluid-heat exchange between the fracture and the matrix is critical. In this paper, we propose a new meshing approach where the fracture grid and the matrix grid operate as two independent systems, featuring either conforming or nonconforming meshes on their shared surface. Then, we derive an edge-cell discretization finite volume method (FVM) algorithm to replace the average approximation approach for computing fluid-heat fluxes between intersecting fractures. Following this, an EGS model is developed to accommodate deformable fracture networks based on the DDM-FVM hybrid algorithm. Finally, we simulate a 3D-EGS model containing five intersecting fractures to investigate the effect of injection/production pressure on total heat extraction. The results reveal several key insights: (1) The new meshing approach allows a coarser fracture grid and a finer matrix grid on the shared surfaces, which has faster computational efficiency; (2) the DDM-FVM hybrid algorithm can well simulate 3D-EGS with deformable and complex fracture networks; (3) fracture deformation significantly influences heat extraction efficiency in EGS during fluid circulation; and (4) increasing either the injection pressure or the production pressure boosts heat extraction efficiency.