Pristine single crystal graphene is the strongest known two-dimensional material, and its nonlinear anisotropic mechanical properties are well understood from the atomic length scale up to a continuum description. However, experiments indicate that grain boundaries in the polycrystalline form reduce the mechanical behavior of polycrystalline graphene. Herein, we perform atomistic-scale molecular dynamics simulations of the deformation and fracture of graphene grain boundaries and express the results as continuum cohesive zone models (CZMs) that embed notions of the grain boundary ultimate strength and fracture toughness. To facilitate energy balance, we employ a new methodology that simulates a quasi-static controlled crack propagation which renders the kinetic energy contribution to the total energy negligible. We verify good agreement between Griffith’s critical energy release rate and the work of separation of the CZM, and we note that the energy of crack edges and fracture toughness differs by about 35%, which is attributed to the phenomenon of bond trapping. This justifies the implementation of the CZM within the context of the finite element method (FEM). To enhance computational efficiency in the FEM implementation, we discuss the use of scaled traction-separation laws (TSLs) for larger element sizes. As a final result, we have established that the failure characteristics of pristine graphene and high tilt angle bicrystals differ by less than 10%. This result suggests that one could use a unique or a few typical TSLs as a good approximation for the CZMs associated with the mechanical simulations of the polycrystalline graphene.