The current work deals with the pulsatile hydromagnetic flow of blood-based couple stress hybrid nanofluid in a porous channel. For hybrid nanofluid, the fusion of gold (Au) and copper oxide (CuO) nanoparticles are suspended to the blood (base fluid). In this model, the employment of viscous dissipation, radiative heat, and Ohmic heating is incorporated. The governing flow equations (set of partial differential equations) are modernized to set of ordinary differential equations by using the perturbation technique. The nondimensional governing equations are solved by adopting the shooting procedure with the help of the Runge–Kutta fourth-order approach. Temperature distributions of hybrid nanofluid and conventional mono nanofluids are portrayed via pictorial results to claim that the hybrid nanofluid has better temperature distribution than mono nanofluids. Temperature is raising for the magnifying viscous dissipation, whereas the reverse behavior can be found with a rise in couple stress parameter. The heat transfer rate is getting high for the higher values of the Eckert number, and the same behavior is noticed with the uplifting magnetic field.