In this work, the capability and performance of the vorticity confinement (VC) implemented in a high-order accurate flow solver in predicting two-dimensional (2D) compressible mixing layer flows on coarse grids are investigated. Here, the system of governing equations with incorporation of the VC in the formulation is numerically solved by the fourth-order compact finite difference scheme. To stabilize the numerical solution, a low-pass high-order filter is applied, and the nonreflective boundary conditions are used at the farfield and outflow boundaries to minimize the reflections. At first, the numerical results without applying the VC are validated by available direct numerical simulations (DNSs) for a low Reynolds number mixing layer. Then, the calculations using a range of VC levels are performed for a high Reynolds number mixing layer and the results are thoroughly compared with those of available large eddy simulations (LESs). The study shows that, with applying the vortex identification method, more accurate results are obtained in the slow laminar region of the mixing layer. A sensitivity study is also performed to examine the effect of different numerical parameters to reasonably provide more accurate results. It is shown that the local VC introduced based on the artificial viscosity coefficient and the vorticity thickness can improve the accuracy of the results in the turbulent region of the mixing layer compared with those of LESs. It is found that the solution methodology proposed can reasonably preserve the vortices in the flowfield and the results are comparable with those of LESs on fairly coarser grids and thus the computational costs can be considerably decreased.