In the context of deep geological disposal of radioactive waste in France, a novel computational framework is developed to model fracture evolution in low-permeability anisotropic rock masses under hydro-mechanical (HM) coupling conditions. The proposed approach integrates explicit fracture representation, anisotropic constitutive behaviour, and coupled HM interaction within a unified numerical scheme. The framework is built upon the Rigid Block Spring Method (RBSM), in which the rock mass is discretized into rigid blocks connected by nonlinear contact elements, enabling explicit simulation of fracture initiation, propagation, and failure and overcoming the limitations of continuum-based approaches in capturing discontinuous deformation processes. To represent the directional dependence of mechanical behaviour in bedded claystone, anisotropic formulations are incorporated at both block and contact levels, allowing elasticity, strength, and fracture evolution to be consistently linked to material anisotropy. To further capture the interaction between fracture evolution and fluid flow, the RBSM framework is coupled with a mixed-dimensional finite element method (MD-FEM) for flow simulation in fractured porous media, enabling HM-consistent analysis during fracture development and incorporation of time-dependent processes such as stress redistribution, pore pressure dissipation, and creep. Numerical examples demonstrate that the proposed framework can effectively reproduce the anisotropic mechanical response of COx rock masses and capture the evolution of fracture networks induced by engineering disturbances. The proposed approach provides a general, extensible, and physically consistent computational framework for investigating HM-coupled fracture evolution in low-permeability anisotropic rock formations.