Self-assembly from the predesigned Cu-5(II) secondary building unit (SBU) in the ternary Cu-II-triazolate-sulfoisophthalate system generates three interesting magnetic samples: an open pillared-layer framework with nanosized Cu-30(II) metallamacrocycle-based sublayer (1), a (3,6)-connected 2-fold interpenetrating network consisting of alternating Cu-5(II) and Cu-II, cores (2), and a (4,8)-connected architecture constructed from centrosymmetric Cu-7(II) clusters and four-branched 5-sulfoisophthalate (sip(3-)) connectors (3). These various structures significantly result from the variable connectivity and the slight expansion of the predetermined conformationally flexible Cu-5(II) SBUs. Furthermore, these intriguing structural motifs in 1-3 essentially induce different magnetic phenomena. A field-dependent metamagnetic transition from antiferromagnetic ordering to weak ferromagnetism is observed in the frustrated Cu-30(II)-based sublayer of 1. The paramagnetic Cu-1(II) core in 2 virtually contributes to an S = 1/2 spin ground state due to the completely compensated magnetic moment in the 1,2,3-triazolate (ta(-))-bridged Cu-5(II) cluster containing ribbon. In contrast, strong antiferromagnetic interactions in the locally centrosymmetric Cu-7(II) cluster lead to an overall S = 1/2 spin ground state of 3. Thus, the SBU-derived self-assembly strategy provides important hints for polymetallic cluster based high-dimensional magnetic materials, which also brings a new vision for the design and construction of novel functional materials.