In wound healing and clinical anti‐infection therapy, the current feasibility of nanocatalysts is extremely limited because of inadequate reactive oxygen species (ROS) generation. Herein, a novel H2O2 self‐supplying nanocomposite (M/C/AEK) consists of molybdenum disulfide (MoS2) decorated with calcium peroxide (CaO2) prepared at ambient temperature and encapsulated in AEK hydrogel. In the presence of H2O2 and poly(vinyl pyrrolidone) (PVP), CaO2 nanoclusters, ≈30 nm, are anchored on the MoS2 surface. MoS2/CaO2 can induce both a cascaded peroxidase (POD)‐like and catalase (CAT)‐like catalytic activity to produce toxic hydroxyl radicals through self‐supplied H2O2 and O2 responsive to the faintly acidic environment of acute wounds. The POD‐like activity is increased under acidic compared with neutral conditions, allowing selective treatment of acute, slightly acidic wounds while avoiding the side effects of high‐concentration antibacterial agents on normal tissues. The high near‐infrared photothermal effect synergistically with POD‐like/CAT‐like activity of MoS2/CaO2 boosts the production of more ROS to eradicate Staphylococcus aureus and Escherichia coli bacteria (98.6% and 98.9%) effectively and selectively stimulate wound healing. The porous M/C/AEK hydrogel in the wound microenvironment can efficiently capture bacteria, and its Ca2+ ions and keratin stimulate healing, revealing excellent potential in advanced wound care and infection control therapies.