<p>The magneto-hemodynamic flow problem is investigated using an innovative and highly effective technique known as the smooth composite pseudo-spectral method. This method employs shifted Chebyshev and shifted Legendre polynomials as basis functions. Rigorous convergence and error analyses validate the proposed scheme. The effects of the Reynolds and Hartmann numbers on magneto-hemodynamic flow in a semi-porous channel are thoroughly examined. Additionally, for varying Reynolds and Hartmann numbers, the maximum residual errors are compared with those obtained from four well-established numerical methods: the differential transform method, the polynomial least squares method, the homotopy perturbation method, and the least squares homotopy perturbation method. Comparative analyses highlight that the proposed technique achieves superior accuracy compared to traditional methods. The effectiveness of this approach in solving magneto-hemodynamic flow problems is clearly demonstrated, suggesting that biomedical engineers and surgeons can improve blood flow control during surgical procedures through precise micromachining of the top plate and the application of a stronger magnetic field.</p>