The nanosecond response of a PbTiO(3)/SrTiO(3) ferroelectric/dielectric superlattice to applied electric fields is closely linked to the dynamics of striped domains of the remnant polarization. The intensity of domain satellite reflections observed with time-resolved x-ray microdiffraction decays in 5-100 ns depending on the magnitude of the electric field. The piezoelectric response of the superlattice within stripe domains is strongly suppressed due to electromechanical clamping between adjacent regions of opposite polarization. Regions of the superlattice that have been switched into a uniform polarization state by the applied electric field, however, exhibit piezoelectricity during the course of the switching process. We propose a switching model different from previous models of the switching of superlattices, based instead on a spatially heterogeneous transformation between striped and uniform polarization states.