Magnetotelluric (MT) sounding is a geophysical technique widely utilized in mineral resource surveys, where conductivity and magnetic permeability serve as essential physical parameters for forward modeling and inversion. However, the effects of conductive anisotropy and non-zero magnetic susceptibility are usually ignored. In this study, we present a three-dimensional (3D) MT modeling algorithm using Coulomb-gauged electromagnetic potentials, incorporating a mixed nodal and edge-based finite element method capable of simulating MT responses for conductive anisotropic and magnetic anomalies. Subsequently, the algorithm’s accuracy was validated in two steps: first, it was compared with analytical solutions for a 1D magnetic model; then, a comparison was made with previously published numerical results for a 3D generalized conductive anisotropic model. The results of two tests show that the maximum relative error is below 0.5% for both models. Furthermore, representative models were computed to comprehensively analyze the responses of MT. The findings illustrate the relationship between anisotropic parameters and electric fields and emphasize the significance of considering the impact of magnetic susceptibility in magnetite-rich regions.