Two-dimensional laminar hemodynamics through a diseased artery featuring an overlapped stenosis was simulated theoretically and computationally. This study presented a mathematical model for the unsteady blood flow with hybrid biocompatible nanoparticles (Silver and Gold) inspired by drug delivery applications. A modified Tiwari-Das volume fraction model was adopted for nanoscale effects. Motivated by the magneto-hemodynamics effects, a uniform magnetic field was applied in the radial direction to the blood flow. For realistic blood behavior, Reynolds’ viscosity model was applied in the formulation to represent the temperature dependency of blood. Fourier’s heat conduction law was assumed and heat generation effects were included. Therefore, the governing equations were an extension of the Navier–Stokes equations with magneto-hydrodynamic body force included. The two-dimensional governing equations were transformed and normalized with appropriate variables, and the mild stenotic approximation was implemented. The strongly nonlinear nature of the resulting dimensionless boundary value problem required a robust numerical method, and therefore the FTCS algorithm was deployed. Validation of solutions for the particular case of constant viscosity and non-magnetic blood flow was included. Using clinically realistic hemodynamic data, comprehensive solutions were presented for silver, and silver-gold hybrid mediated blood flow. A comparison between silver and hybrid nanofluid was also included, emphasizing the use of hybrid nanoparticles for minimizing the hemodynamics. Enhancement in magnetic parameter decelerated the axial blood flow in stenotic region. Colored streamline plots for blood, silver nano-doped blood, and hybrid nano-doped blood were also presented. The simulations were relevant to the diffusion of nano-drugs in magnetic targeted treatment of stenosed arterial diseases.