The successful transport of drug- and cell-based therapeutics to diseased sites represents a major barrier in the development of clinical therapies. Targeted delivery can be mediated through degradable biomaterial vehicles that utilize disease biomarkers to trigger payload release. Here, we report a modular chemical framework for imparting hydrogels with precise degradative responsiveness by using multiple environmental cues to trigger reactions that operate user-programmable Boolean logic. By specifying the molecular architecture and connectivity of orthogonal stimuli-labile moieties within material cross-linkers, we show selective control over gel dissolution and therapeutic delivery. To illustrate the versatility of this methodology, we synthesized 17 distinct stimuli-responsive materials that collectively yielded all possible YES/OR/AND logic outputs from input combinations involving enzyme, reductant and light. Using these hydrogels we demonstrate the first sequential and environmentally stimulated release of multiple cell lines in well-defined combinations from a material. We expect these platforms will find utility in several diverse fields including drug delivery, diagnostics and regenerative medicine.