Molecular dynamics (MD) simulation is applied to investigate the mechanical response of AlCrCuFeNi high-entropy alloy (HEA) under the conventional cutting and ultrasonic elliptical vibration-assisted cutting (UEVAC). The influences of vibration frequency, amplitude ratio, and phase angle on the material removal mechanism are investigated. The results show that the strain and stress are concentrated on the contact area between the workpiece and cutting tool, as well as at the grain boundaries in both cutting methods. The temperature of workpiece under the UEVAC is significantly larger than the conventional cutting, which can have a positive impact on the phase transformation and makes UEVAC easier. The analysis of structure and dislocation exposes that the deformation behavior of polycrystalline is strongly influenced by the grain boundaries, the evolution of stacking fault and dislocation is obstructed by the grain boundaries. Moreover, the average cutting force of the UEVAC is reduced as rising the vibration frequency and amplitude ratio, while the average force under the UEVAC with various phase angles has no significant difference. The number of chip atoms shows that the material removal rate is greater under the UEVAC with a larger vibration frequency, lower amplitude ratio and phase angle. The plastic deformation of chip becomes more serious under the UEVAC with a vibration frequency of 150 GHz, amplitude ratio of 4, and phase angle of 75° due to the smallest cutting ratio. The figure shows the physical model (a), von Mises stress clouds (b) and relationship of force-cutting length (c) of AlCrCuFeNi HEA under the conventional cutting (b1 and c1) and UEVAC with vibration frequency of 150 GHz (b2 and c2). Display omitted •The mechanism of UEVAC and the conventional nano-cutting method are exhibited and compared.•Effects of vibration frequency, amplitude ratio and phase angle on deformation behavior of AlCrCuFeNi HEA are investigated.•The cutting forces of UEVAC and conventional nanocutting show significant differences.•The UEVAC can produce the higher material removal rate compared to conventional cutting.