Timber construction is increasingly shaped by automation, promising gains in precision, efficiency, and safety. However, contemporary digital fabrication methods typically rely on standardized lumber and rigid workflows, limiting their capacity to integrate diverse, irregular, and reclaimed resources–essential for reducing carbon emissions. Advancing more sustainable construction practices requires systems that are less linear and more adaptive, capable of effectively managing material variability. We introduce Truss From Trash, a human-robot collaboration framework for the adaptive assembly of timber trusses using irregular wood offcuts. The system enables real-time negotiation between available materials and evolving design intent, allowing users to make adjustments while robots take on the repetitive, precise, and hazardous tasks of picking, cutting, and placing components. At the core of the framework is a projection-based interface that overlays visual feedback directly onto the worktable, situating interaction within the fabrication context. Users engage with the system by physically manipulating custom 3D printed tokens, each representing a design operation, to explore design alternatives by adjusting the geometry or the topology of the truss. We validate the system through a series of fabrication experiments that demonstrate how the framework fosters creative, in-context decision-making in direct response to the constraints and opportunities presented by the available materials. The work repositions material uncertainty not as an obstacle to overcome, but as a catalyst for design exploration, and reimagines design as an ongoing, situated process that unfolds through the dynamic interplay of human creativity, construction tools, and the materials at hand.