We investigate the ultimate strengths and failure types of asymmetric tilt grain boundaries (GBs) with various tilt angles with the aid of molecular dynamics simulations and analytic theory. The tensile strength of armchair-oriented graphene GBs shows a tendency to increase as the misorientation angle rises, while that of zigzag-oriented graphene GBs non-monotonically increases. The overall strength enhancement and weakening behaviors can be explained by a continuum stress analysis of pentagon-heptagon defects along GBs. Nevertheless, full atomistic analyses are required to predict the exact bonds from which mechanical failure initiate. Two different fracture types are observed in our studies; one with cracks growing along the GB and another with cracks growing away from the GB. Detailed understanding of the atomic arrangement along the GB, in addition to defect density, is necessary to ascertain the ultimate strength and rupture process of GBs.