In this paper, we study the interesting phenomena of stress waves attenuation and impact energy dissipation by the application of multi-resonator dissipative acoustic metamaterials (DAMs) with Kelvin–Voigt-type (KVT), Maxwell-type (MT) and Zener-type (ZT) oscillators. The theoretical analyses show that these microstructures have broad negative effective mass frequency regions and high effective metadamping coefficient. The numerical results prove that the damping characteristics can gather the multiple band gaps of the elastic multi-resonator metamaterial together. KVT oscillators present the best performances in impact load mitigation and collision energy dissipation among these DAMs. With very small damping coefficients, the attenuation and dissipation effects of MT models are poor, and the performances of ZT and KVT models are similar. By properly tailoring the damping, the performances of KVT and MT are significantly improved. Meanwhile, the influence of damping on the performances of ZT oscillators is less compared with KVT and MT models.