A novel elastic mechanical metamaterial with extreme damping performance has been achieved skillfully by coupling snap-through and pseudo-constant-force behaviors. The proposed meta-damping mechanism is systematically expounded to tailor synthetical force–displacement response for programming hyper energy dissipations. Within this framework, detailed designs in functional sub-structures and collaborative design strategy combined with parametric optimization in integrated structure are further presented synthetically. By additive manufacturing and loading–unloading cyclic experiments, the physical realization of meta-damping elastic metamaterials reveals the extraordinary specific damping capacity (Ψ=7.03), which exceeds any research reported previously and is immensely close to the theoretical limit. Remarkably, this minimalist design method, with only two necessary functional components, reconciles the contradiction between load-bearing and damping dissipation, with strong multi-directional and periodic expansibility. This work has far-reaching implications on the compact design of recoverability, reusability, frequency-independent, material-independent elastic mechanical metamaterials for superior dynamic applications such as impact absorption, vibration reduction, and energy trapping.