Three extended three-dimensional (3D) magnetic metal-organic frameworks (MMOFs), {[Mn3(H2O)2(atz)4Cl2]·2CH3OH}n (1), {[Mn2(H2O)(atz)2(ip)]·C2H5OH}n (2) and {[Mn2(H2O)2(atz)(btc)]·3H2O·0.7CH3OH}n (3) (atz(-) = 5-aminotetrazolate, ip(2-) = isophthalate and btc(3-) = 1,3,5-benzenetricarboxylate), were respectively obtained by varying the coligands with different numbers of functionalities and molecular topology, and structurally and magnetically characterized. Complex 1 exhibits an eight-connected 3(6)·4(18)·5(3)·6 topological network with linear Mn(II)3 subunits periodically linked by ditopic atz(-) connectors. Complex 2 possesses a pillared-layer framework constructed from undulated {Mn2(atz)2} layers and bidirectional ip(2-) spacers. By contrast, 3 consists of bent one-dimensional (1D) {Mn(atz)} ribbons, which are crosslinked through the carboxylate groups of tripodal btc(3-) connectors to generate a 3D architecture. Structural analysis reveals that the interesting motifs of 1-3 and their diverse linkages are significantly dominated by the cooperate coordination of the mixed ligands to the octahedral Mn(II) ion. Magnetically, 1 displays ferrimagnetic behavior resulting from the periodic arrangement of the net moment in the Mn(II)3 subunit, which is scarcely observed in the homometallic azolate systems. Complex 2 features unusual coexistence of spin-canted antiferromagnetic behavior and field-induced spin-flop transition due to the asymmetric magnetic superexchange within the two-dimensional (2D) {Mn2(atz)2} sublayer. By contrast, only antiferromagnetic ordering is observed in the 1D {Mn(atz)} ribbon of 3. These interesting results suggest that the diverse structural motifs by the cooperate coordination of octahedral Mn(II) ion with the N-rich tetrazolyl group can more significantly direct the magnetic behaviors and could be hopefully utilized upon the construction of novel MMOFs.