Rock failure progressive processes in static tests and dynamic impact tests are modelled using a hybrid finite-discrete element method. The simulated results are then compared with these recorded in literatures to calibrate the hybrid method. After that, the hybrid finite-discrete element method is applied to model rock excavation in mechanical cutting. Throughout this study, it is concluded that the hybrid finite-discrete element method is superior to the continuum-based finite element method and the discontinuum-based discrete element method in terms of modelling rock failure progressive process and resultant fragment flow, and may be a valuable numerical tool for optimizing the design of rock cutting and drilling equipments.