We theoretically show that terahertz pulses with controlled amplitude and frequency can be used to switch between stable transport modes in layered superconductors, modeled as stacks of Josephson junctions. We find pulse shapes that deterministically switch the transport mode between superconducting, resistive, and solitonic states. We develop a simple model that explains the switching mechanism as a destabilization of the center-of-mass excitation of the Josephson phase, made possible by the highly nonlinear nature of the light-matter coupling.