We investigate the physicomechanical properties of polymeric heterogeneous catalysts of transition-metal oxides, specifically, the specific surface area, elongation at break, breaking strength, specific electrical resistance, and volume resistivity. Digital microscopy, Fourier-transform infrared spectroscopy, X-ray diffraction, scanning electron microscopy, and energy-dispersive analysis are used to study the surfaces of the catalysts. The experimental results show that polymeric heterogeneous catalysts of transition-metal oxides exhibit high stability and can maintain their catalytic activity under extreme reaction conditions for long-term use. The oxidation mechanism of sulfur-containing compounds in the presence of polymeric heterogeneous catalysts of transition-metal oxides is confirmed. Microstructural characterization of the catalysts is performed by using X-ray computed tomography. The activity of various catalysts in the oxidation of sulfur-containing compounds is determined. We demonstrate the potential application of polymeric heterogeneous catalysts of transition-metal oxides in industrial wastewater treatment.