The MINERvA collaboration operated a scaled-down replica of the solid scintillator tracking and sampling calorimeter regions of the MINERvA detector in a hadron test beam at the Fermilab Test Beam Facility. This article reports measurements with samples of protons, pions, and electrons from 0.35 to 2.0 GeV/c momentum. The calorimetric response to protons, pions, and electrons are obtained from these data. A measurement of the parameter in Birks law and an estimate of the tracking efficiency are extracted from the proton sample. Overall the data are well described by a Geant4-based Monte Carlo simulation of the detector and particle interactions with agreements better than 4%, though some features of the data are not precisely modeled. These measurements are used to tune the MINERvA detector simulation and evaluate systematic uncertainties in support of the MINERvA neutrino cross section measurement program.