Dual-ferrofluid or hybrid ferrofluid, with unique thermal and magnetic properties, are valuable in biomedical applications for precise, magnetically guided drug delivery and thermotherapy, especially in cancer treatment. The present study aims to investigate the behaviour of dual-ferrofluid \({Fe}_{3}{O}_{4}/{CoFe}_{2}{O}_{4}\) mixed with ethylene glycol and water over a slip-extending sheet under the influence of magnetoviscous effect (MVE). The governing equations are first simplified into ordinary differential equations using suitable similarity variables. The numerical solutions are then obtained using the MATLAB solver bvp4c. The analysis reveals that the MVE parameter enhances both the velocity and temperature fields. The shear stress of the dual-ferrofluid decreases by 12.73%, whereas the Nusselt number increases by 6.65% due to MVE. Furthermore, the slip velocity reduces the fluid velocity but enhances the thermal boundary layer. The dual-ferrofluid demonstrates a more prominent effect in the thermal field compared to the mono-ferrofluid flow. This indicates that MVE and slip velocity may alter drug delivery using dual-ferrofluid flow.