Irradiation with high-energy electrons (HEE) at cryogenic temperatures is a subtle tool for shaping matter. Unlike irradiation with heavy particles, e.g. protons, neutrons, or ions, HEE irradiation produces very low local damage generating exclusively point lattice defects. In the interaction process, the primary high-energy electron transfers a minute quantity of energy to a lattice ion, just enough for displacing it from its lattice site. The concentration of induced vacancies depends on the irradiation dose and in this way can be carefully adjusted. Since the lattice defects can act as donor or acceptor states in semiconductors, electron irradiation enables accurately-controlled compensation of electrically-active impurities introduced in a semiconductor crystal during growth. In this article, we present a study of the evolution of electronic properties of β-gallium oxide with step-by-step compensation of initial n-type doping through controlled introduction of point defects (gallium vacancies) produced by a 2.5-MeV electron beam. Our analysis relies on a set of electron paramagnetic resonance, luminescence, and transport data obtained at different temperatures.