In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to the multi-species gas mixture and multiscale plasma transport. The construction of the scheme is based on the direct modeling on the mesh size and time step scales, and the local cell's Knudsen number determines the flow physics. The proposed scheme has the multiscale and asymptotic complexity diminishing properties. The multiscale property means that according to cell's Knudsen number the scheme can capture the non-equilibrium flow physics in the rarefied flow regime, and preserve the asymptotic Euler, Navier-Stokes, and magnetohydrodynamics limit in the continuum regime. The asymptotic complexity diminishing property means that the total degree of freedom of the scheme automatically decreases as cell's Knudsen number decreases. In the continuum regime, the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver. In UGKWP, the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables, and the particle evolution as well as the macroscopic fluxes are modeled from the time accumulating solution up to a time step scale from the kinetic model equation. For plasma transport, current scheme provides a smooth transition from particle in cell (PIC) method in the rarefied regime to the magnetohydrodynamic (MHD) solver in the continuum regime. In the continuum limit, the cell size and time step of the UGKWP method is not restricted to be less than the mean free path and mean collision time. In the highly magnetized regime, the cell size and time step are not restricted by the Debye length and plasma cyclotron period. The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.