A vibration absorber combining the acoustical black hole (ABH) effect with vibro-impacts is presented as a separate device that can be mounted on a primary structure for passive vibration mitigation. The vibration isolator is shown to be effective for low-frequency shock vibration attenuation. Numerical and experimental results are reported, considering a rectangular honeycomb plate as the primary structure, on which the device, consisting of a circular ABH plate with one or several impact masses, is attached. A numerical model is developed using a finite element space discretisation combined with a conservative scheme in a penalty approach for the contact dynamics. The analysis shows that the device has broadband efficiency thanks to the combined effects of energy transfer due to impacts and high attenuation in mid and high-frequency range due to the ABH effect. A detailed parametric study underlines that the tuning of the linear fundamental frequency of the impact mass plays an important role. Besides, considering several impact masses is shown to improve the efficacy. An experimental setup is then used in order to demonstrate the effectiveness of the device. The results confirm the vibration mitigation trends obtained from the numerical model that could then be used as a designed tool for the attenuator. Finally, an analysis based on the Shock Response Spectrum (SRS), widely used in the field of aerospace engineering, is performed, underlining the attenuator is able to reduce rapidly and efficiently the vibrations due to a mechanical shock.