Abstract: In order to reveal the evolution of droplet propulsion, deformation, and fragmentation in supersonic and hypersonic environment, a conservative sharp-interface multiphase method is used to simulate the shock-droplet interaction with high-Mach and extremely high-Mach numbers. The numerical results are in good agreement with the experimental results, which indicates the accuracy of the numerical method and the corresponding computer code. The grid independence study demonstrates that the grid resolution used in this paper can capture the main features of the flow field and interface. The numerical results verify the shear-induced entrainment (SIE) breaking mechanism followed by the droplet deformation and fragmentation under high-Weber number, including two main features, i.e. the flattening of droplets and the shearing of the sheet at the droplet equator. The recently discovered recurrent breakup mechanism under the SIE mechanism has also been verified in this paper. The initial spherical-droplet is deformed, and breaks into smaller sub-droplets via recurrent rupture stages. And the fragmentation of droplets for high-Weber number is indeed not the result of one single shearing process, but rather occurs recurrently. The effect of the Mach number on the shock-droplet interaction is also investigated here. Our results indicate that the droplet fragmentation process for different Mach numbers is highly analogous, following the general SIE mechanism. The time evolution of the dimensionless center-of-mass drift, velocity, acceleration, and drag coefficient reveal the unified acceleration tendency for droplet under shock impact. In addition, the droplet does not propel with a constant acceleration rate for the whole stage. Instead, when the flattening effect is absent in early stage, the droplet accelerates at a constant acceleration. As the flattening occurs, the increase of the upwind area leads to an increase in the drag coefficient, which in turn increases acceleration rate of the droplet movement.