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A series of heterometallic carboxylate 1D polymers of the general formula [LnIIICd2(piv)7(H2O)2]n·nMeCN (LnIII = Sm (1), Eu (2), Tb (3), Dy (4), Ho (5), Er (6), Yb (7); piv = anion of trimethylacetic acid) was synthesized and structurally characterized. The use of CdII instead of ZnII under similar synthetic conditions resulted in the formation of 1D polymers, in contrast to molecular trinuclear complexes with LnIIIZn2 cores. All complexes 1–7 are isostructural. The luminescent emission and excitation spectra for 2–4 have been studied, the luminescence decay kinetics for 2 and 3 was measured. Magnetic properties of the complexes 3–5 and 7 have been studied; 4 and 7 exhibited the properties of field-induced single-molecule magnets in an applied external magnetic field. Magnetic properties of 4 and 7 were modelled using results of SA-CASSCF/SO-RASSI calculations and SINGLE_ANISO procedure. Based on the analysis of the magnetization relaxation and the results of ab initio calculations, it was found that relaxation in 4 predominantly occurred by the sum of the Raman and QTM mechanisms, and by the sum of the direct and Raman mechanisms in the case of 7.