In rock engineering, blasting works are often carried out near the existing underground caverns, like tunnels, mine roadways and storage caverns. Moreover, the natural fractures and joints within rock mass are also inevitable. In order to explore the characteristics of rock fragmentation in blasting scenarios for jointed rock mass of underground space, four series of bonded particle models were created with an opening and a set of preexisting discontinuities. The crack propagation process was evaluated with the principal stress evolution, contact forces between particles and the particle velocity as well as changes in the discontinuity inclination angle. For the specimens containing horizontal and vertical discontinuities, it is found that cracks firstly initiate from the borehole and the time of crack initiation and peak stress comes latter. However, for the specimens containing inclined discontinuities, cracking starts from the discontinuity immediately after detonation. It is found that the proposed numerical method is useful in depicting the fragmentation features of rock with discontinuities under blasting disturbance.