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We experimentally demonstrate efficient switching of the hard x-ray Bragg reflectivity of a SrRuO3 /SrTiO3 superlattice by optical excitation of large-amplitude coherent acoustic superlattice phonons. The rocking curve changes drastically on a 1 ps timescale. The (0 0 116) reflection is almost extinguished (Delta R/R-0=-0.91), while the (0 0 118) reflection increases by more than an order of magnitude (Delta R/R-0=24.1). The change of the x-ray structure factor depends nonlinearly on the phonon amplitude, allowing manipulation of the x-ray response on a timescale considerably shorter than the phonon period. Numerical simulations for a superlattice with slightly changed geometry and realistic parameters predict a switching-contrast ratio Delta R/R-0 of 700 with high reflectivity.