Click chemistries are efficient and selective reactions that have been leveraged for multi-stage drug delivery. A multi-stage system allows independent delivery of targeting molecules and drug payloads, but targeting first-phase materials specifically to disease sites remains a challenge. Stimuli-responsive systems are an emerging strategy where common pathophysiological triggers are used to target payloads. Oxidative stress is widely implicated in disease, and we have previously demonstrated that reactive oxygen species (ROS) can crosslink and immobilize polyethylene glycol diacrylate (PEGDA) in tissue mimics. To build on these promising results, we present a two-step, catch-and-release system using azide-DBCO click chemistry and demonstrate the capture and eventual release of a fluorescent payload at defined times after the formation of a PEGDA capturing net. The azide component is included with radical-sensitive PEGDA, and the payload is conjugated to the DBCO group. In cell-free and cell-based tissue mimic models, azides were incorporated at 0–30% in the first-phase polymer net, and DBCO was delivered at 2.5–10 µM in the second phase to control payload delivery. The payload could be captured at multiple timepoints after initial net formation, yielding a flexible and versatile targeting system. Matrix metalloproteinase (MMP)-degradable peptides were incorporated into the polymer backbone to engineer fluorescent payload release by MMPs, which are broadly upregulated in diseases, through degradation of the capture net and directly from the DBCO. Taken together, this research demonstrates proof-of-principle for a responsive and clickable biomaterial to serve as a multi-potent agent for the treatment of diseases compounded by high free radicals.