This article presents an analysis and the resulting limits on light dark matter inelastically scattering off of electrons, and on dark photon and axion-like particle absorption, using a second-generation SuperCDMS high-voltage eV-resolution detector. The 0.93 gram Si detector achieved a 3 eV phonon energy resolution; for a detector bias of 100 V, this corresponds to a charge resolution of 3% of a single electron-hole pair. The energy spectrum is reported from a blind analysis with 1.2 gram-days of exposure acquired in an above-ground laboratory. With charge carrier trapping and impact ionization effects incorporated into the dark matter signal models, the dark matter-electron cross section $bar{sigma}_{e}$ is constrained for dark matter masses from 0.5--$10^{4} $MeV$/c^{2}$; in the mass range from 1.2--50 eV$/c^{2}$ the dark photon kinetic mixing parameter $varepsilon$ and the axioelectric coupling constant $g_{ae}$ are constrained. The minimum 90% confidence-level upper limits within the above mentioned mass ranges are $bar{sigma}_{e},=,8.7times10^{-34}$ cm$^{2}$, $varepsilon,=,3.3times10^{-14}$, and $g_{ae},=,1.0times10^{-9}$.
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