<p>Advances in data-driven design and additive manufacturing have substantially accelerated the development of truss metamaterials—three-dimensional truss networks—offering exceptional mechanical properties at a fraction of the weight of conventional solids. While existing design approaches can generate metamaterials with target linear properties, such as elasticity, they struggle to capture complex nonlinear behaviours and to incorporate geometric and manufacturing constraints—including defects—crucial for engineering applications. Here we present GraphMetaMat, an autoregressive graph-based framework capable of designing three-dimensional truss metamaterials with programmable nonlinear responses, originating from hard-to-capture physics such as buckling, frictional contact and wave propagation, along with arbitrary geometric constraints and defect tolerance. Integrating graph neural networks, physics biases, imitation learning, reinforcement learning and tree search, we show that GraphMetaMat can target stress–strain curves across four orders of magnitude and vibration transmission responses with varying attenuation gaps, unattainable by previous methods. We further demonstrate the use of GraphMetaMat for the inverse design of novel material topologies with tailorable high-energy absorption and vibration damping that outperform existing polymeric foams and phononic crystals, potentially suitable for protective equipment and electric vehicles. This work sets the stage for the automatic design of manufacturable, defect-tolerant materials with on-demand functionalities.</p>