Methanol is a promising renewable fuel for achieving a better engine combustion efficiency and lower exhaust emissions. Under exhaust gas recirculation conditions, trace amounts of nitrogen oxides have been shown to participate in fuel oxidation and impact the ignition characteristics significantly. Despite numerous studies that analyzed the methanol/NOx interaction, no reliable skeletal kinetic mechanism is available for computational fluid dynamics (CFD) modeling. This work focuses on developing a skeletal CH3OH/NOx kinetic model consisting of 25 species and 55 irreversible and 27 reversible reactions, used for full-cycle engine combustion simulations. New experiments of methanol with the presence of 200 ppmv NO/NO2 were conducted in a rapid compression machine (RCM) at engine-relevant conditions (20-30 bar, 850-950 K). Experimental results indicate notable enhancement effects of the presence of NO/NO2 on methanol ignition under the conditions tested, which highlights the importance of including the CH3OH/NOx interactions in predicting combustion performance. The proposed skeletal mechanism was validated against the literature and new methanol and methanol/NOx experiments over a wide range of operating conditions. Furthermore, the skeletal mechanism was applied in three-dimensional (3D) CFD full-cycle simulations of spark-ignition (SI) and turbulent jet ignition (TJI) engine combustion using methanol. Simulation results demonstrate good agreement with experimental measurements of pressure traces and engine metrics, proving that the proposed skeletal mechanism is suitable and sufficient for CFD simulations.