Direct numerical simulations of high-speed mixing layers are used to characterize the effects of compressibility on the basis of local streamline topology and vortical structure. Temporal simulations of the mixing layers are performed using a finite volume gas-kinetic scheme for convective Mach numbers ranging from Mc=0.2 to Mc=1.2. The focus of the study is on the transient development and the main objectives are to (i) investigate and characterize the turbulence suppression mechanism conditioned upon local streamline topology; and (ii) examine changes in the vortex vector field - distribution, magnitude and orientation - as a function of Mach number. We first reaffirm that kinetic energy suppression with increasing Mach number is due to a decrease in pressure-strain redistribution. Then, we examine the suppression mechanism conditioned upon topology and vortex structure. Conditional statistics indicate that (i) at a given Mach number, shear-dominated topologies generally exhibit more effective pressure-strain redistribution than vortical topologies; and (ii) for a given topology, the level of pressure-strain correlation mostly decreases with increasing Mach number. At each topology, with increasing Mach number, there is a corresponding decrease in turbulent shear stress and production leading to reduced kinetic energy. Further, as Mc increases, the proportion of vortex-dominated regions in the flow increases, leading to further reduction in the turbulent kinetic energy of the flow. Then, the orientation of vortical structures and direction of fluid rotation are examined using the vortex vector approach of Tian et al. (J. Fluid Mech., vol. 849, 2018, pp. 312-339). At higher Mc, the vortex vectors tend to be more aligned in the streamwise direction in contrast to low Mc wherein larger angles with streamwise direction are preferred. The connection between vortex orientation and kinetic energy production is also investigated. The findings lead to improved insight into turbulence suppression dynamics in high Mach number turbulent flows. © 2019 Cambridge University Press.