Bifunctional 1,2,4-triazole-carboxylate ligands, an achiral 1,2,4-triazol-4-yl-acetic acid (trgly-H) and a chiral (d)-2-(1,2,4-triazol-4-yl)-propionic acid (d-trala-H), derived from the corresponding α-amino acid precursors revealed unique binding abilities in the construction of Cu(II)-coordination polymers composing discrete triangular [Cu3(μ3-OH)] clusters. A related series of MOFs, [Cu3(μ3-OH)(trgly)3(SO4)]·2H2O (1a), [Cu3(μ3-OH)(trgly)3(H2O)3]SO4·16H2O (1b), Cu3(μ3-OH)(d-trala)3(ClO4)0.5](ClO4)1.5·1.5H2O (2), was prepared, and their crystal structures were determined by means of X-ray diffraction. Being singly deprotonated, the organic ligands act as multidentate μ3- or μ4-donors using tr and -COO(-) moieties. The generated [Cu3(μ3-OH)(tr)3] cluster core is primarily supported by three [-N-N-] triazole heterocycles in a basal plane and tripodal-assisted μ3-anions (SO4(2-): 1a; ClO4(-): 2) capping the axial faces. The carboxylate groups join the units into either two-dimensional (2D) layer (1a, 2) or 3D zeolite-like networks (1b). Compound 1b represents the topology of α-Po (pcu: 4(12).6(3)) and crystallizes in the noncentrosymmetric space group I4̅3m, in which the six-connected [Cu3(μ3-OH)] clusters and trgly self-assemble in an open-channel cubic array possessing ∼56% solvent-accessible volume. Upon slight thermal treatment (∼60 °C), the structure irreversibly shrinks to the nonporous 2D motif 1a that belongs to a uninodal (3,6) network type. In structure 2 (space group R32), due to the [-N-N-] triazole and 1,3-bidentate carboxylate binding mode, each organic ligand bridges three metal clusters affording cross-linking of two adjacent layers with the same (3,6) topology. The resultant 3,9-c net is novel and can be categorized as two-nodal with point symbol {4(18).6(18)}{4(2).6}3. Spin frustration and antisymmetric exchange effects, resulting in abnormally low g values in the S = 1/2 states, were observed in the magnetic properties and the EPR spectra.