Two 5‐methyl‐tetrazolate (mtz–)‐based paramagnetic metal coordination polymers, {[Cu2(H2O)2(mtz)(μ3‐OH)(nip)]·H2O}n (1) and [Cu(H2O)(mtz)2]n (2), were obtained in the presence and absence of aromatic 5‐nitroisophathalate (nip2–) coligand by varying the preparation methods. Structural determinations reveal that 1 is a three‐dimensional (3D) framework with corner‐sharing triangular ribbons infinitely extended by ditopic nip2– connectors. In contrast, 2 is a coplanar (4,4) layer constructed from square‐pyramidal CuII ions and μ‐N1,N4‐mtz– linkers, which is further assembled into a 3D supramolecular network by interlayer hydrogen‐bonding interactions. Magnetically, spin‐frustrated antiferromagnetic ordering is observed in the 3D framework of 1 and canted antiferromagnetic behavior with a slight spin‐flop transition is presented in 2, which are structurally resulting from the locally Δ‐ribbon in 1 and asymmetric magnetic superexchange mediated by the μ‐N1,N4‐mtz– bridge of 2.