High-pressure torsion (HPT) was applied to a lamellar eutectic high-entropy alloy (EHEA) to study the effect of severe plastic deformation (SPD) on the composite structure and mechanical properties. We found that the existence of multiple phases affects defect distribution and the fragmentation process during HPT. Structural evolution shows orientation dependence with respect to the shear plane, which finally leads to a refined multiphase structure with nanograins and vortex clusters after a shear strain γ of 24. In nanograins, dislocation-mediated deformation prevails. The high density of grain boundaries, forest dislocations, and the generation of deformation twins restrict dislocation movement. As a result, an EHEA with a yield strength of 1.75 GPa, an excellent tensile strength of 2.20 GPa, and an appreciable failure strain of 5 % is realized. Our results demonstrate that the HPT deformation process of the lamellar EHEA is significantly affected by the structure. SPD on the multiphase structure is a suitable route for designing high-strength yet ductile alloys.