This work is devoted to the numerical study of mixing two miscible liquid metals, e.g., Sn and Pb, that are driven either separately by a rotating magnetic field (RMF), by a traveling magnetic field (TMF), or by a combination of both fields from the state of rest. The geometry studied is an enclosed cylindrical cavity with an aspect ratio equal to unity (the diameter of the cylinder is equal to its height, 2R ₀ = H ₀). The initial condition is a cylinder with the lower half filled with a melt that has two times the molecular viscosity of the liquid in the upper part of the cavity. Based on the mixture model of the two-fluid flow and the axisymmetric Navier-Stokes equations, the transient transport of momentum as well as the species for rotary and axial stirring is modeled. The numerical simulations were performed under microgravity conditions for Ekman numbers between 10 ^-3 and 10 ^-4 for the RMF-driven flow and for Reynolds numbers between 100 and 400 for TMF-driven flow that corresponded to both laminar and weak turbulent flows. The simulations analysis showed that for RMF, the rapid increase in the mixing rate occurs because of randomly appearing Taylor-Görtler vortices that move up and down along the side wall of the cylinder and that dissipate in the Bödewadt layers. The TMF stirring with forcing parameters that produced laminar flow offers a better mixing performance than the RMF stirring at the same magnetic field intensity. However, with an increase in magnetic forcing, the RMF and TMF lead to comparable mixing times for the same value of magnetic field induction. Additionally, we discuss different mixing scenarios that include the use of time-modulated RMF and TMF. Numerical simulations showed that the discontinuous superposition of RMF and TMF-defined as the sequential switching on and off of both fields with a well-defined period-enhances the mixing in comparison with the non-superimposed case.