Developing physical double‐network (DN) removable hydrogel adhesives with both high healing efficiency and photothermal antibacterial activities to cope with multidrug‐resistant bacterial infection, wound closure, and wound healing remains an ongoing challenge. An injectable physical DN self‐healing hydrogel adhesive under physiological conditions is designed to treat multidrug‐resistant bacteria infection and full‐thickness skin incision/defect repair. The hydrogel adhesive consists of catechol–Fe 3+ coordination cross‐linked poly(glycerol sebacate)‐ co ‐poly(ethylene glycol)‐ g ‐catechol and quadruple hydrogen bonding cross‐linked ureido‐pyrimidinone modified gelatin. It possesses excellent anti‐oxidation, NIR/pH responsiveness, and shape adaptation. Additionally, the hydrogel presents rapid self‐healing, good tissue adhesion, degradability, photothermal antibacterial activity, and NIR irradiation and/or acidic solution washing‐assisted removability. In vivo experiments prove that the hydrogels have good hemostasis of skin trauma and high killing ratio for methicillin‐resistant staphylococcus aureus (MRSA) and achieve better wound closure and healing of skin incision than medical glue and surgical suture. In particular, they can significantly promote full‐thickness skin defect wound healing by regulating inflammation, accelerating collagen deposition, promoting granulation tissue formation, and vascularization. These on‐demand dissolvable and antioxidant physical double‐network hydrogel adhesives are excellent multifunctional dressings for treating in vivo MRSA infection, wound closure, and wound healing.