The development of safe, fast-acting, and pressure-free biomedical adhesives remains a key challenge for internal tissue sealing, where current cyanoacrylate and fibrin-based products are limited by heat generation, toxicity, and weak wet adhesion. Here, we report a photocurable biomedical adhesive that integrates catechol chemistry, thiol–ene UV curing, and disulfide exchange to achieve strong adhesion in wet and mucosal environments. The adhesive, synthesized from eugenol-derived catechol monomers and multifunctional thiols, forms a cross-linked network with poly(ethylene glycol) dimethacrylate under UVA (350 nm) irradiation within 1 min. The resulting polymer exhibits strong and flexible adhesion to diverse substrates, with dry adhesion strengths of 164 kPa, comparable to cyanoacrylate-based superglues but an order of magnitude higher work of adhesion, indicating a tougher and more compliant interface. Under wet conditions, the adhesive maintains 144 kPa strength on porcine skin-polypropylene interfaces and 56 kPa underwater, outperforming commercial fibrin adhesives. Flow cytometry analysis of NIH-3T3 cells exposed to the adhesive for 72 h revealed minimal increases in dead-cell populations, with overall viabilities remaining above 96%, demonstrating excellent cytocompatibility. Overall, this study demonstrates a fast-curing, biocompatible, and versatile adhesive platform that combines bulk cohesion, wet adhesion, and covalent mucoadhesion for next-generation biomedical applications.