An approach for particle breakage simulation based on the framework of discrete element method was proposed in the current study. Convex polyhedron blocks were adopted as elementary particles for the complex particle shapes, and the variability of particle breakage strength is modeled using the invertible function method. Additionally, the traditional modified “Brazilian” criterion was adopted as the breakage criterion. Under the assumption that the eventual fractures within a particle can be determined according to the contact points and the centroid of the particle, once a target particle fulfilled the breakage criterion, it was cut into several fragments by a series of virtual cutting faces, which are consistent with the eventual fractures. With this, the production of local stress and the non-conservation of mass and volume can be avoided. A pre-defined fragmentation mode was also unnecessary for this approach. A series of numerical triaxial tests adopting this new presented approach was then conducted according to the configurations reported in the literature and comparisons made with experimental results. It revealed that while the presented approach is capable of reproducing the macroscopic shear responses and particle breakage characteristics of breakable particle assemblies, some fragmentation modes of particles such as surface grinding and corner abrasion cannot be captured using this approach, presenting an area for future investigation.