We have obtained an excitation of longitudinal bulk acoustic waves in a diamond-based High overtone Bulk Acoustic Resonator (HBAR) at microwave and enhanced frequency bands as EHF up to 40 GHz. As an effective piezoelectric transducer, an aluminum-scandium nitride film is employed. The frequency response of acoustic overtones excited in the HBARs with a different aperture in the 1.0 up to 40 GHz range is measured. Some peculiarities of HBAR's frequency response concerned with the thin film piezoelectric transducer are studied. It is established that the maximal magnitude of the quality factor varies near the value of about 10 000 within all the frequency bands investigated. The approximately frequency-independent Q-factor behavior can explain in terms the Landau–Rumer approximation describing the acoustic attenuation in a diamond. An estimation of the HBAR's quality parameter as Q × f ≈ 4 × 1014 Hz at 40 GHz is obtained. In our opinion, that value exceeds all known data among the given devices. The results obtained will be helpful in the development of microwave and EHF acoustic resonators as well as highly sensitive acoustic sensors. The development of the EHF band opens up the possibility of obtaining acoustic waves of submicrometer and nanometer scales (in various media) and implementing acoustic studies of micro- and nanoobjects.