In the current landscape of natural gas hydrate extraction, the lifting pump assumes a pivotal role as the essential equipment for conveying subsea fluidized hydrate slurry to the wellhead. The inherent shear-thinning characteristics of natural gas hydrate slurry, compounded by the complex multiphase flow conditions of the “gas-liquid-solid” system, present significant challenges to the operational efficiency and stability of the lifting pump. Consequently, this study adopts a hybrid approach, combining experimental and numerical simulations, to comparatively investigate the impact of non-Newtonian and viscous Newtonian fluids on the hydraulic performance, vortex structure evolution, and induced pressure fluctuations in a multiphase pump. Concurrently, a comparative analysis is conducted on the influence of these two fluid types on the distribution patterns of the “gas-solid” two-phase system. The research findings indicate that the apparent viscosity variations are more pronounced in the diffuser region compared to the impeller region. Under non-Newtonian fluid conditions, two separation vortices emerge at the trailing edge of the diffuser, as opposed to a single separation vortex in the viscous Newtonian fluid, with the latter exhibiting a smaller vortex structure scale. Moreover, the shear-thinning characteristics intensify the interaction between the separated vortex and the mainstream, resulting in an exacerbation of pressure fluctuations. In contrast to the viscous Newtonian fluid, the rotor–stator interaction and shear-thinning characteristics play a predominant role in pressure fluctuations, with shear-thinning attributes giving rise to low-frequency pressure fluctuations. Additionally, shear-thinning characteristics significantly influence the distribution behavior of the gas-solid two-phase flow.