The path of crack propagation in a graphene sheet is significant for graphene patterning via the tearing approach. In this study, we evaluate the fracture properties of pre-cracked graphene during the tearing process, with consideration of the effects of the aspect ratio, loading speed, loading direction, and ambient temperatures on the crack propagation in the monolayer sheet. Some remarkable conclusions are drawn based on the molecular dynamic simulation results, i.e., a higher loading speed may result in a complicated path of crack propagation, and the propagation of an armchair crack may be accompanied by sp carbon links at high temperatures. The reason for this is that the stronger thermal vibration reduces the load stress difference near the crack tip and, therefore, the crack tip can pass through the sp link. A crack propagates more easily along the zigzag direction than along the armchair direction. The out-of-plane tearing is more suitable than the in-plane tearing for graphene patterning. The path of crack propagation can be adjusted by changing the loading direction, e.g., a rectangular graphene ribbon can be produced by oblique tearing. This new understanding will benefit the application of graphene patterning via the tearing approach.