General features of ring-opening metathesis copolymerization, accompanied by macromolecular cross-metathesis, are studied by kinetic Monte Carlo simulations. Despite the successful commercialization of metathesis polymers, which have found applications as both structural and functional materials, the role of cross-reactions during polymer synthesis and processing remains poorly understood. In this paper, a series of simulations is performed for a binary system to describe the evolution of the reaction active centers, polymerization degree, and block length distributions. The model is parameterized using experimental data on the interaction of norbornene with cyclooctene in the presence of Grubbs’ ruthenium initiator. It is shown that the early stage is dominated by the propagation of polynorbornene chains, which maintain a narrow molar mass distribution, whereas the polymerization of cyclooctene occurs later, being considerably affected by cross-reactions. The blockiness parameter of copolymer chains reaches its maximum of about 0.5 at the moment when all initial monomers are exhausted, after which it slowly decreases to its stationary value. This final state does not necessarily correspond to a fully random copolymer and can be accurately predicted based on the combination of four rate coefficients describing the elementary cross-metathesis reactions. The relaxation rate was found to increase with norbornene content, since it facilitates the formation of heterodyads via the reaction between polynorbornene-based carbenes and double bonds in spatially unconstrained cyclooctene homodyads. Furthermore, the model is demonstrated to capture initiator deactivation and to reproduce two-stage polymerization schemes, wherein the components are polymerized separately and subsequently combined to generate copolymers with controlled microstructure.