We present here a design of the unit cell of a mechanical metamaterial based on the use of a tensegrity structural configuration with a metal rubber. Tensegrity combines the use of compression and tension-only elements, and allows the creation of structures with high rigidity per unit mass. Metal rubber is a multiscale porous metal material with high energy absorption and vibration damping capabilities under compressive load. The combination of the two structural and material concepts gives rise to a mechanical metamaterial with increased energy absorption and tuneable nonlinearity under quasi-static, vibration, and impact loading. We develop prototypes, models, and perform tests under static and dynamic loading conditions to assess the performance of this mechanical metamaterial.