Buckling, which was once considered the epitome of design failure, has been harnessed during the last few years to develop mechanical metamaterials with advanced functionalities. Soft robotics in general and soft actuators in particular could greatly benefit from such designer materials. Unlocking the great potential of buckling-driven materials is, however, contingent on resolving the main limitation of the designs presented to date, namely the limited range of their programmability. Here, we present multi-material buckling-driven metamaterials with high levels of programmability. We combined rational design approaches based on predictive computational models with advanced multi-material additive manufacturing techniques to 3D print cellular materials with arbitrary distributions of flexible and stiff materials in the central and corner parts of their unit cells. Using the geometry and spatial distribution of material properties as the main design parameters, we developed soft mechanical metamaterials behaving as mechanisms whose actuation force and actuation amplitude could be adjusted both independently and concomitantly within wide ranges. Our designs also resulted in the emergence of a new lowest instability mode, i.e. double-side buckling, in addition to the already known modes of side-buckling and symmetric compaction. Finally, we proposed a general approach to pre-dispose our soft mechanical metamaterials such that they can reliably actuate their higher instability modes without any need for additional boundary conditions or fixtures. To demonstrate this approach, we created a cellular mechanism with a rotational buckling pattern that clones the functionality of mechanical machines. The potential of the presented designs in robotics is then demonstrated by applying them as a force switch, kinematic controllers, and a pick and place end-effector.