Mimetic finite difference (MFD) approximations of continuous gradient and divergente operators satisfy a discrete version of the Gauss-Divergente theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP). In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC) with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD) stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite differene method.