Four magnetic samples with different building blocks and dimensionalities, {[Cu(4)(atr)(2)(μ(3)-OH)(2)(sip)(2)]·4H(2)O}(n) (1), {[Cu(4)(atr)(2)(H(2)O)(8)(μ-OH)(2)(sip)(2)]·1.3CH(3)OH·0.7H(2)O}(n) (2), {[Cu(3)(atr)(4)(H(2)O)(2)(sip)(2)]·4H(2)O}(n) (3) and {[Cu(3)(atr)(4)(H(2)O)(2)(μ(3)-OH)(sip)(Hsip)]·2CH(3)OH·2.75H(2)O}(n) (4) (atr = 4-amino-1,2,4-triazole and sip(3-) = 5-sulfoisophthalate), were obtained and characterized structurally and magnetically. Complex 1 exhibits a three-dimensional (3D) robust framework with butterfly-like Cu(II)(4) clusters periodically extended by tetratopic sip(3-) connectors. Complex 2 possesses a 2D layer with alternating Cu(II)(3) + Cu(II)(1) chains crosslinked by pairs of ditopic sip(3-) linkers. By contrast, the latter two entities feature 1D broad ribbons with linear (for 3) and triangular Cu(II)(3) cores (for 4) propagated by bidirectional sip(3-) connectors. Structural analysis reveals that the diverse building blocks and dimensionalities of 1-4 are significantly dominated by the tunable coordination of exocyclic amino- and/or sulfonate-group of the mixed ligands. Magnetically, antiferromagnetic interactions with variable strength transmitted by -NN- moiety of atr and hydroxyl mediators result in overall S = 0 (for 1) and 1/2 (for 3 and 4) spin ground states. These interesting results indicate that coordinative side group in the ternary metal ion-azolate-carboxylate system can be utilized to generate aesthetically pleasing building units and variably polytopic connectors, leading to differently extended superstructures and magnetic behavior.