During CO2-enhanced shale gas recovery (CO2-ESGR), the competitive adsorption and flow characteristics of binary CO2/CH4 in shale reservoirs significantly influence both CH4 production and CO2 storage. However, the coupled mechanisms involving competitive adsorption-induced swelling and slippage effect, and their impact on the evolution of reservoir permeability, remain poorly understood. This study investigated variations in deformation and permeability of shale induced by the adsorption of pure and binary gases (CH4, CO2, CO2/CH4 = 1:2, 2:1). A permeability model incorporates the coupling influences of competitive adsorption, slippage effect and effective stress was developed, and the factors influence shale permeability were analyzed. As the gas pressure increased, the CH4/CO2 competitive adsorption-induced swelling strain of shale showed two stages variation trend of increased rapidly and slowly. Correspondingly, the permeability showed a trend of rapid decreased first and then gradual increased. This process was also affected by the CO2 molar fraction and the stress. Using the developed permeability model, it can be revealed that the impact of the shale permeability increase caused by the slippage effect gradually weakened as the pressure increased, while the impact of the shale permeability decrease induced by the competitive adsorption-induced swelling typically initially intensified and then subsequently weakened. Furthermore, the impact of the shale permeability decrease induced by the effective stress and competitive adsorption-induced swelling to permeability weakened as increasing confining pressure or decreasing CO2 molar fraction, whereas the slippage effect's impact intensified. The flow behavior of a variety of gas molecules within shale is primarily influenced by variations in pore size that are the result of competitive adsorption and effective stress, as well as the differences in the average free path of different gases. These findings provide a theoretical foundation for optimizing CO2-ESGR.