Purpose <p>This study proposes a programmable piezoelectric energy harvester based on an auxetic cantilever architecture incorporating a functionally graded graphene-origami auxetic metamaterial (FG-GOAM) core. The research aims to quantify the power-output enhancement relative to conventional harvesters, enabled by the coupled effects of graphene-origami negative Poisson’s ratio (NPR) behavior, folding-induced stiffness modulation, and spatial material grading.</p> Methods <p>A bridge-type auxetic metamaterial piezoelectric cantilever with a tip mass is developed, where the FG-GOAM substrate is sandwiched between two piezoelectric layers. The harvester substrate consists of a copper matrix integrated with graphene-origami (GOri) reinforcements to form a metal-based architected metamaterial. The auxetic response is tuned through layer-wise variation of graphene content and folding degree across the thickness. A generalized electromechanical model is formulated using the Lagrange method, and analytical solutions are obtained for natural frequencies, voltage response, and power–frequency characteristics. Parametric analyses examine the influence of material gradation, tip-mass geometry, and electrical load resistance.</p> Results <p>The graded graphene-origami architecture enables significant resonance tunability and improves electromechanical coupling efficiency. Under identical operating conditions, the proposed harvester produces approximately 10% higher output power than a conventional copper-substrate counterpart.</p> Conclusion <p>The FG-GOAM auxetic cantilever provides an effective route toward programmable vibration energy harvesting and demonstrates the promise of graphene-based architected composites for adaptive, self-powered engineering systems.</p>