A series of four new Dy12 dodecanuclear clusters based on azobenzene derivative ligands of salicylic acid (L1-L4) has been synthesized and characterized in the crystalline phase using X-ray diffraction on single crystal and powder, IR spectroscopy, elemental analysis, and DSC-TGA methods. It was revealed that all obtained clusters exhibit the formation of the similar metallic cluster nodes, as vertex-sharing heterocubanes, obtained from four Dy3+ cations, three bridging hydroxyl groups, and O atoms from the salicylic ligands. The coordination geometry around the Dy(III) centers has been carefully analyzed. Whereas Dy12-L1 and Dy12-L2 with L1 and L2 containing Me and OMe groups in para positions of the phenyl rings, respectively, form similar porous 3D diamond-like molecular networks due to CH-π interactions, for Dy12-L3 with L3 bearing NO2-electron-withdrawing group, the generation of 2D molecular grids assembled by π-π staking is observed, and for Dy12-L4 with L4 bearing phenyl substituent, 3D hexagonal channels have been generated. The complexes Dy12-L1, Dy12-L2, and Dy12-L3 exhibit a zero-field slow magnetic relaxation effect. After UV irradiation of Dy12-L1, a decrease of the magnetic anisotropy energy barrier displaying the possibility of control over magnetic properties by the external stimulus has been observed.