Contraction and expansion play a crucial role in biomedical applications, such as heart pumping, ovum in the feminine fallopian vessel, blood fluid transport, and so forth. Inspired by these features, the present effort concentrates on the consequences of a thermal slip in the peristalsis of Cu/blood and Cu-CuO/blood nanofluids in asymmetric flow formation. Hence, the microrotation influence of blood flow is considered here. Heat transported through the channel due to perpendicular flow buoyancy effects is also studied. The special effects of thermal radiation, nanoparticle shape, and heat source/sink parameters on the flow are studied in the proposed model. The MATLAB BVP4c condition is utilized to achieve the numerical solutions of the transformed system of nonlinear coupled differential equations. The most important outcome of the present analysis is an enhancement in the evaluation study of the Cu/blood and Cu-CuO/blood nanofluids on the axial velocity, axial spin velocity, pressure gradient, and temperature distributions in the asymmetric channel. Also, another important outcome is observed that the Cu-CuO blood nanofluid strongly has dominated the Cu/blood nanofluid in axial spin velocity.