The understanding of crack formation due to applied stress is key to predicting the ultimate mechanical behavior of many solids. Here we present experimental and theoretical studies on cracks or tears in suspended monolayer graphene membranes. Using transmission electron microscopy, we investigate the crystallographic orientations of tears. Edges from mechanically induced ripping exhibit straight lines and are predominantly aligned in the armchair or zigzag directions of the graphene lattice. Electron-beam induced propagation of tears is also observed. Theoretical simulations account for the observed preferred tear directions, attributing the observed effect to an unusual nonmonotonic dependence of graphene edge energy on edge orientation with respect to the lattice. Furthermore, we study the behavior of tears in the vicinity of graphene grain boundaries, where tears surprisingly do not follow but cross grain boundaries. Our study provides significant insights into breakdown mechanisms of graphene in the presence of defective structures such as cracks and grain boundaries.