A fluid-driven fracture propagation model dominated by viscosity-leak-off regime was presented to investigate the mechanical stability of natural fracture (NF) when hydraulic fracture (HF) approaches. The induced stresses generated by the approaching HF were calculated by a fully coupled integro-differential equation. The pore pressure effect caused by fracturing fluid leak-off was simulated based on dual porosity medium theory. The critical failure conditions of NF were determined based on maximum tensile criterion and Barton-Bandis criterion. The sensitivity of the stability of NF to in-situ stress anisotropy, approaching angle and distance, injection rate, fracturing fluid viscosity, and NF properties was analyzed in detail. Simulation results reveal that the shearing-mode failure of NF is obviously easier than the opening-mode failure, and the shear slip zone is much larger than the tensile failure zone. As HF approaches NF non-orthogonally, the induced debonding process is unstable, and the debonding zone is asymmetric with respect to the center of NF. The tensile-induced expansion zone is primarily located in the portion of NF ahead of the HF tip, however the shear-induced slip zone can even occur on NF behind of the HF tip. Induced stresses alone have negligible effect on the stability of the NF that is unconnected to the HF. The change in pore pressure due to leak-off effect dominates the final stimulated reservoir volume during large-scale fracturing. The instability of the NF dominates the propagation trajectory of the subsequent HF. A more suitable arrested/crossing condition by extending Gu-Weng criterion was established to predict the path of HF propagation.