A Dy(III) coordination polymer (CP), [Dy(spasds)(H2O)2]n (1) (Na2Hspasds = 5-(4-sulfophenylazo)salicylic disodium salt), has been synthesized using a hydrothermal method and characterized. 1 features a 2D layered structure, where the spasda3− anions act as pentadentate ligands, adopting carboxylate, sulfonate and phenolate groups to bridge with four Dy centers in η3-μ1: μ2, η2-μ1: μ1, and monodentate coordination modes, respectively. It possesses a unique (4,4)-connected net with a Schläfli symbol of {44·62}{4}2. The luminescence study revealed that 1 exhibited a broad fluorescent emission band at 392 nm. Moreover, the visual blue color has been confirmed by the CIE plot. 1 can serve as a dual-functional luminescent sensor toward Fe3+ and MnO4− through the luminescence quenching effect, with limits of detection (LODs) of 9.30 × 10−7 and 1.19 × 10−6 M, respectively. The LODs are relatively low in comparison with those of the reported CP-based sensors for Fe3+ and MnO4−. In addition, 1 also has high selectivity and remarkable anti-interference ability, as well as good recyclability for at least five cycles. Furthermore, the potential application of the sensor for the detection of Fe3+ and MnO4− was studied through simulated wastewater samples with different concentrations. The possible sensing mechanisms were investigated using Ultraviolet-Visible (UV-Vis) absorption spectroscopy and density functional theory (DFT) calculations. The results revealed that the luminescence turn-off effects toward Fe3+ and MnO4− were caused by competitive absorption and photoinduced electron transfer (PET), and competitive absorption and inner filter effect (IFE), respectively.