The efficient separation of CO2 from CH4 and N2 is essential for the upgrading of biogas and reducing carbon emissions in flue gas, but is challenging in the energy industry. Developing ultra-stable adsorbents with high CO2 adsorption performance in adsorption separation technology is deemed an effective solution for the separation of CO2/CH4 and CO2/N2. Herein, we report an ultra-stable yttrium-based microporous metal-organic framework (Y-bptc) used for the efficient separation of CO2/CH4 and CO2/N2. The single-component equilibrium adsorption capacity of CO2 reached 55.1 cm3 g-1 at 1 bar and 298 K, while the adsorption capacity of CH4 and N2 was almost negligible and thus resulted in a high adsorption ratio for CO2/CH4 (45.5) and CO2/N2 (18.1). GCMC simulations revealed that the μ3-OH- functional groups distributed in the pore cage of Y-bptc provide stronger adsorption sites for CO2via hydrogen-bonding interactions. The relatively lower heat of adsorption of CO2 (24 kJ mol-1) further reduces the desorption regeneration energy consumption. Dynamic breakthrough experiments using Y-bptc for the separation of CO2/CH4 (1/1) and CO2/N2 (1/4) mixtures could obtain high purity (>99%) CH4 and N2, and the CO2 dynamic adsorption capacities reached 52 and 31 cm3 g-1, respectively. More importantly, the structure of Y-bptc remained intact under hydrothermal conditions. The high adsorption ratio, low heat of adsorption, great dynamic separation performance, and ultra-stable structure of Y-bptc make it one of the candidate adsorbents suitable for the separation of CO2/CH4 and CO2/N2 in real-world applications.