This paper assesses the potential of coherent vortex simulation (CVS) to compute three-dimensional turbulent mixing layers. CVS splits each turbulent flow realization into two orthogonal parts, one corresponding to coherent vortices which are kept, and the other to an incoherent background flow which is discarded. The CVS filter is applied to data from direct numerical simulations (DNS) of three-dimensional forced and unforced time-developing turbulent mixing layers. The coherent flow is represented by few wavelet modes, but these are sufficient to reproduce the vorticity probability distribution function and the energy spectrum out to the high-wavenumber end of the inertial range. The discarded incoherent background flow is homogeneous, small-amplitude and decorrelated. The CVS-filtering results are then compared with those obtained for the same compression ratio using Fourier low-pass filtering, as employed in large-eddy simulation (LES). Compared to the incoherent background flow of CVS filtering, the subgrid scales of LES filtering are less homogeneous, have much larger amplitude, and exhibit spatial correlations that makes modelling them a difficult challenge. Finally we present simulations of a time-developing mixing layer where the CVS filter is applied at each time step. The results show that CVS preserves the nonlinear dynamics of the flow, and that discarding the incoherent modes is sufficient to model turbulent dissipation.