This paper proposes an explicit-incremental Finite-Element formulation and implementation approach for studying the nonlinear coupling of magneto-mechanical properties and the response of Terfenol-D, a giant magnetostrictive material. The approach is based on experimental data or relevant constitutive models and depicts the nonlinear variations of magnetostrictive materials' properties in different prestress levels and bias magnetic field intensity through piecewise interpolation. The Finite-Element and incremental formulation are given by means of weak form equations, and numerical examples are performed in ABAQUS. The explicit interpolation eliminates general iterations in many other numerical methods, making this approach more efficient. A numerical stability verification is needed to calibrate a proper increment. The numerical results demonstrate high accuracy and stability, simulating the magnetostrictive response in different prestress levels and magnetic field intensity exactly and efficiently. It reports the influence of prestress on maximal magnetostrictive strains, i.e., "the reversal phenomenon," providing theoretical and practical significance in designing and applying magnetostrictive devices or conducting nonlinear magneto-mechanical coupling analysis.