In this research, a discrete modelling approach employing a new cohesive model is proposed to investigate the failure response of cemented materials. A cohesive model considering mixed-mode fracture is developed based on a generic thermodynamic framework for coupling damage mechanics and plasticity theory. Discrete Element Method (DEM), a well-known computational method for simulating large deformation and cracking issues, is utilised as a numerical platform to facilitate the implementation of the proposed cohesive model. The nature of discrete modelling is analogous to the internal structure of cemented materials, making it more efficient compared with conventional continuum methods to characterise the failure behaviour of cemented materials. This combined cohesive-discrete modelling approach is then employed to simulate four experimental tests under different boundary conditions. Simulation results show excellent agreements with the experiments in terms of both macro force-displacement responses and cracking patterns, suggesting the effectiveness of the proposed modelling approach for conducting numerical experiments and exploring the failure mechanisms in cemented materials.