We discuss the search for boosted dark matter scattered off either electron or proton in the Deep Underground Neutrino Experiment. We particularly focus on the case where such boosted dark matter up-scatters to a heavier dark-sector unstable state which subsequently decays back to the dark matter and additional visible particles. The benchmark model to describe the interactions between the Standard Model and dark-sector particles includes a dark photon. We study the experimental sensitivity to the relevant signal in the plane of the dark photon mass and the kinetic mixing parameter.