The cornerstone of mimetic finite differentiation (FD) is that discrete gradients and divergences, in combination with a novel boundary flux operator satisfies an approximation to the Gauss–Divergence theorem. In this paper, we propose a spatially staggered second-order discretization of the acoustic wave equation that fully exploits all these mimetic operators on the implementation of free surface and absorbing boundary conditions. Explicit time integration is carried out by using the standard three-level central FD stencil. Applications of this new method to simple 2-D seismic scenarios are also presented and discussed.