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There are essentially two different approaches to producing methane from natural gas hydrate reservoirs, either bring the hydrate out of its thermodynamic stability region or expose the hydrate to a substance that will form a more stable hydrate structure, forcing an in situ swapping of the trapped gas molecules in the structural lattice. In this work, we quantitatively investigate the swapping behavior from injection of pure carbon dioxide and the (CO2 + N2) binary gas mixture through artificial hydrate-bearing sandstone samples by use of a core-flooding experimental apparatus. A total of 13 experimental runs were performed to examine the influence of operating conditions on methane production by CO2/(CO2 + N2) injection in the temperature range of 274.15–277.15 K and 7.039–10.107 MPa pressure. Our results show that the use of the (CO2 + N2) binary gas mixture is advantageous compared to the use of pure carbon dioxide in swapping methane from its hydrate phase; the methane recovery efficiency in brine water systems is enhanced relative to pure water systems. The replenishment of a fresh (CO2 + N2) gas mixture into the vapor phase can be considered as an efficient extraction method because 46.32% of methane was displaced from its hydrate phase with the (CO2 + N2) binary gas mixture after 341.75 h of exposure to the (CO2 + N2) gas mixture. During the CH4–(CO2 + N2) swapping process, gas chromatography analysis and calculations demonstrated that nitrogen molecules can take the place of some methane in small hydrate cages, as long as the equilibrium formation pressure of (CO2 + N2) binary gas hydrate is below that of methane hydrate, even though adding nitrogen to carbon dioxide reduces the thermodynamic driving force for the formation of a new hydrate. When other conditions are similar, the methane gas recovery efficiency increases with the increase of the driving force for the swapping process.