The mechanical behavior of AlCuNiTi alloy during orthogonal micro-cutting consists of conventional cutting and complex-dimensional vibration cutting (CDVC) are investigated using molecular dynamics (MD). The material removal mechanism is studied in terms of phase angle, amplitude ratio, and vibration frequency. In both techniques, the stress and strain are localized in the contiguous location between the sample and the cutting tool. The sample temperature during CDVC is noticeably greater than during classical cutting, which might benefit the transition phase and make CDVC smoother. The total mean value cutting force of the CDVC decreases as the frequencies of vibration and ratios of amplitude increase; however, the mean values of force under the CDVC with different phase angles demonstrate hardly ever statistically significant change. The quantity of atoms in the chip indicates that the machined surface rate is higher under the CDVC, with a higher frequency of vibration, smaller phase angle, and amplitude ratio. Under CDVC, the chip of plastic deformation gets more pronounced and severe with a frequency of oscillation at 150 GHz, an amplitude at 1.5, and a phase angle degree of 75○ due to the lowest cutting ratio.