The paper presents the results of measuring the spectral and dose characteristics of pulse-periodic X-ray radiation generated by a plasma accelerator. The device is based on the principle of electron autophasing in the oscillating electric field of a microwave cavity, implemented in the scenario of automatic maintenance of electron cyclotron resonance in a magnetic field that slowly increases in time in the interaction region (gyromagnetic autoresonance, GA). It was found that electrons of generated plasma bunches during acceleration reach energies of up to 0.5 MeV. Due to multiple acceleration and deceleration of electrons in the microwave field, hard X-ray radiation is generated, which is of interest for radiation technologies. It is shown that the bremsstrahlung of bunches has a pronounced anisotropy and spatial regions with its maximum output are experimentally determined. The measured average absorbed dose rate for biological tissue was 2 mGy/s. Conditions for increasing the accelerator’s bremsstrahlung power with an increase in the number of accelerated electrons and their energy are determined. The accompanying characteristic radiation of the plasma-forming gas and the accelerator’s structural elements facing the plasma is investigated.