The separation of CO2/CH4 gas mixtures is a key challenge for the energy sector and is essential for the efficient upgrading of natural gas and biogas. A new emerging field, that of metal-organic framework nanosheets (MONs), has shown the potential to outperform conventional separation methods and bulk metal-organic frameworks (MOFs). In this work, we model the CO2/CH4 separation in both defect-free and defective 2D CuBDC nanosheets and compare their performance with the bulk CuBDC MOF and experimental data. We report the results of external force nonequilibrium molecular dynamics (EF-NEMD) for pure components and binary mixtures. The EF-NEMD simulations reveal a pore blocking separation mechanism, in which the CO2 molecules occupy adsorption sites and significantly restrict the diffusion of CH4. The MON structure achieves a better selectivity of CO2 over CH4 compared to the bulk CuBDC MOF which is due to the mass transfer resistance of the methane molecules on the surface of the nanosheet. Our results show that it is essential to consider the real mixture in these systems rather than relying solely on pure component data and ideal selectivity. Furthermore, the separation is shown to be sensitive to the presence of missing linker defects in the nanosheets. Only 10% of missing linkers result in nonselective nanosheets. Hence, the importance of a defect-free synthetic method for CuBDC nanosheets is underlined.