In this work, three unique TbIII-carboxylate frameworks with the formula {[Tb2(OH)2(H2O)2(abtc)]·2H2O}n (1), {[Tb2(abtc)1.5(H2O)3(DMA)]·H2O}n (2) and {[Tb3(abtc)2.5(H2O)4]·H3O}n (3), each displaying structural variations, have been successfully synthesized by the solvothermal reactions of Tb(NO3)3·6H2O with the azo-containing ligand 3,3',5,5'-azobenzene tetracarboxylic acid (H4abtc) under varying conditions. Detailed single-crystal X-ray diffraction (SC-XRD) analysis manifested a remarkable diversity in these structures, demonstrating various coordination patterns of TbIII-metal nodes with the carboxylate groups of the organic linker, which contributed to the generation of intricate three-dimensional (3D) coordination networks with remarkable chemical resistance. Furthermore, frameworks 2 and 3, characterized by porous networks containing two and three independent TbIII-metal nodes, respectively, were both demonstrated to be efficient heterogeneous catalysts toward the cyanosilylation of imines under mild conditions with excellent reusability. In addition, direct current (Dc) magnetic susceptibility measurements conducted on frameworks 1, 2, and 3 indicated that there were obvious antiferromagnetic interactions among the TbIII-metal nodes, which suggests the involvement of intricate intra- and intertrimer exchange channels, adding another fascinating dimension to their physical properties.