The planetary motion of impeller in the vertical mixer can effectively promote the dispersed circulation and homogeneous distribution of different material components， which has been employed in the preparation procedure of solid propellant slurry. However， the mixer involves complex interfaces and motions that it is difficult to study the mixing mechanism and rheological property of slurries by traditional methods. Based on the smoothed particle hydrodynamics （SPH）， the continuum was discretized into the conserved particles with physical quantities for simulating the interaction between the propellant slurry and blades under laminar flow. A meshless method for the mixing process of propellant slurries in non-Newtonian fluid state was developed by combining the Herschel-Bulkley （HB） constitutive model. The numerical simulations were compared with the experiments to verify the accuracy of the proposed model. The correlations of the blade motion parameters and power consumption were explored. The effects of geometric configurations and rotation modes on the mixing uniformity of slurries and the torque loads of impellers were analyzed. Research findings indicate that the simulation and literature experiment results have a good agreement that the average relative error between them is around 4.98% in the non-Newtonian fluid with shear rate index n=0.47. The mixing uniformity index of planetary impellers increased by 8.9% and 7.3% respectively than those of central and eccentric impellers after stirring for 2.65 s. The maximum amplification in torque can reach 38.4% within the revolution radius range of 0.11D_w-0.23D_w at Reynolds number Re=1.