Two low-dimensional oxime-containing Schiff base copper(I/II) complexes with iodine–copper cluster [Cu₂I₄]²⁻ bridges, namely, {[Cu^II₄I₃(pop)₄]₂(Cu^I₂I₄)}·(CH₃CN)₂·H₂O (2) and [Cu^II₄I₂(pop)₄(Cu^I₂I₄)·(CH₃CN)]_n (3) (Hpop = 2-(hydroxyimino)-N′-[1-(2-yridyl)ethylidene]propanehydrazone), have been synthesized from the reaction of [2 × 2] grid-like compound {[Cu^III(pop)]₄}₂·4H₂O (1) with equivalent Cu^I₂I₂ (iodine–copper clusters) under solvothermal conditions and characterized by elemental analysis (EA), infrared spectroscopy (IR), thermogravimetric analysis (TGA), and X-ray single-crystal/powder diffraction. The results show that 2 is a 0-D discrete structure from an assembly of one [Cu₂I₄]²⁻ unit and two [2 × 2] molecular grids (1) via μ₃-I atoms coordinating to Cu^I/Cu^II atoms. However, compound 3 presents a 1-D wave-like chain, which is constructed by coordination of μ₂-I atoms from [Cu^I₂I₄]²⁻ units with Cu^II atoms in [2 × 2] molecular grids (1). Moreover, catalytic experiments demonstrated that compounds 2 and 3 have promising visible-light-driven catalytic activity in degrading various organic dyes.