To conduct a more in-depth study of the flow mechanism of power-law fluids within sewage pumps, this paper focuses on self-priming sewage pumps, with typical power-law fluid (Carboxymethyl Cellulose, CMC) as the conveying medium. The constitutive equations for sewage and typical power-law fluid (CMC solution) were established using the power-law model. Through numerical calculation methods, the non-steady flow field inside the pump of different concentration power-law fluids was analyzed from various aspects such as velocity, pressure, vorticity, and wall shear stress. The pressure pulsations at key locations in the pump flow field were monitored and analyzed. At the rated flow rate, when the concentration of CMC solution increased from 0.5% to 2.0%, the channel pressure and tongue pressure decreased by 16.5% and 3.5%, respectively. This indicates that the pressure on the impeller blades, within the flow passages, and at the tongue of the volute all decrease with the increase in concentration of CMC solution. This may alter the fluid flow pattern, leading to more vortex motion and shear deformation, while also reducing the pump’s pressure boosting capability, thereby affecting the pump’s performance stability. It can be inferred from quantitative comparisons that changes in rheological properties had a significant impact on the flow characteristics of sewage pumps. This paper reveals that some flow characteristics of power-law fluids in sewage pumps, providing a theoretical and reference basis for the performance optimization and flow mechanism research of sewage pumps.