In this work, we report the synthesis of SION-8, a novel metal-organic framework (MOF) based on Ca(II) and a tetracarboxylate ligand TBAPy(4-) endowed with two chemically distinct types of pores characterized by their hydrophobic and hydrophilic properties. By altering the activation conditions, we gained access to two bulk materials: the fully activated SION-8F and the partially activated SION-8P with exclusively the hydrophobic pores activated. SION-8P shows high affinity for both CO2 (Q(st) = 28.4 kJ/mol) and CH4 (Q(st) = 21.4 kJ/mol), while upon full activation, the difference in affinity for CO2 (Q(st) = 23.4 kJ/mol) and CH4 (Q(st) = 16.0 kJ/mol) is more pronounced. The intrinsic flexibility of both materials results in complex adsorption behavior and greater adsorption of gas molecules than if the materials were rigid. Their CO2/CH4 separation performance was tested in fixed-bed breakthrough experiments using binary gas mixtures of different compositions and rationalized in terms of molecular interactions. SION-8F showed a 40-160% increase (depending on the temperature and the gas mixture composition probed) of the CO2/CH4 dynamic breakthrough selectivity compared to SION-8P, demonstrating the possibility to rationally tune the separation performance of a single MOF by manipulating the stepwise activation made possible by the MOF's biporous nature.