We report numerical simulation results of a recently proposed [P. Bruno, Phys. Rev. Lett 79, 4593 (1997)] approach to perform magnetic scanning tunneling microscopy with a two terminal nonmagnetic tip. It is based upon the spin asymmetry effect of the tunneling current between a ferromagnetic surface and a two-terminal nonmagnetic tip. The spin asymmetry effect is due to the spin-orbit scattering in the tip. The effect can be viewed as a Mott scattering of tunneling electrons within the tip. To obtain quantitative results we perform numerical simulations within the single-band tight-binding model, using the recursive Green's-function method and the Landauer-Böttiker formula for conductance. A model has been developed to take into account the spin-orbit scattering off the impurities within the single-band tight-binding model. We show that the spin-asymmetry effect is most prominent when the device is in the quasiballistic regime and the typical value of spin asymmetry is about 5%.