In this study, we use the extended finite element method (XFEM) with a consideration of junction enrichment functions to investigate the mechanics of hydraulic fractures related to naturally cemented fractures. In the proposed numerical model, the lubrication equation is adopted to describe the fluid flow within fractures. The fluid-solid coupling systems of the hydraulic fracturing problem are solved using the Newton-Raphson method. The energy release rate criterion is used to determine the cross/arrest behavior between a hydraulic fracture (HF) and a cemented natural fracture (NF). The failure patterns and mechanisms of crack propagation at the intersection of natural fractures are discussed. Simulation results show that after crossing an NF, the failure mode along the cemented NF path may change from the tensile regime to the shear or mixed-mode regime. When an advancing HF kinks back toward the matrix, the failure mode may gradually switch back to the tensile-dominated regime. Key factors, including the length of the upper/lower portion of the cemented NF, horizontal stress anisotropy, and the intersection angle of the crack propagation are investigated in detail. An uncemented or partially cemented NF will form a more complex fracture network than a cemented NF. This study provides insight into the formation mechanism of fracture networks in formations that contain cemented NF.