We report the synthesis, structure, and adsorption properties of two new metal–organic frameworks (MOFs) {[Cu2(bpp)3(L1)]·(bpp)·(4H2O)} (1) and {[Cu2(bipy)2(L2)(H2O)2]·(bipy)·(5H2O)} (2) obtained from two different flexible tetracarboxylate linkers (L1 and L2) of variable lengths and flexibility. While 1 comprising CuII, L1, and 1,3-bis(4-pyridyl) propane (bpp) is a 2D MOF with a cage-type structure, 2 consisting of CuII, L2, and 4,4′-bipyridine (bipy) has a 3D twofold interpenetrated structure. Both frameworks manifest permanent porosity, as realized from CO2 adsorption at 195 K. 2 shows excellent CO2/N2 and C2H2/C2H4 adsorption selectivity at 298 K. This has been established by using 2 as a separating medium in a breakthrough column for separating mixtures of CO2/N2 (15:85, v/v) and C2H2/C2H4 (1:99, v/v). The selectivity of 2 toward CO2 over N2 and C2H2 over C2H4 is governed by favorable thermodynamic interactions owing to its structural flexibility, unsaturated metal sites, and polar carboxylate groups. Thus, 2 proves to be an extremely efficient material for specific gas separation.