Nanozymes, emerging nanomaterials for wound healing, exhibit enzyme-like activity to modulate the levels of reactive oxygen species (ROS) at wound sites. Yet, the solo regulation of endogenous ROS by nanozymes often falls short, particularly in chronic refractory wounds with complex and variable pathological microenvironments. In this study, we report the development of a multifunctional wound dressing integrating a conventional alginate (Alg) hydrogel with a newly developed biodegradable copper hydrogen phosphate (CuP) nanozyme, which possesses good near-infrared (NIR) photothermal conversion capabilities, sustained Cu ion release ability, and pH-responsive peroxidase/catalase-mimetic catalytic activity. When examining acute infected wounds characterized by a low pH environment, the engineered Alg/ CuP composite hydrogels demonstrated high bacterial eradication efficacy against both planktonic bacteria and biofilms, attributed to the combined action of catalytically generated hydroxyl radicals and the sustained release of Cu ions. In contrast, when applied to chronic diabetic wounds, which typically have a high pH environment, these composite hydrogels exhibit significant angiogenic performance. This is driven by the provision of catalytically generated dissolved oxygen and a beneficial supplement of Cu ions released from the degradable CuP nanozyme. Further, a mild thermal effect induced by NIR irradiation amplifies the catalytic activities and bioactivity of Cu ions, thereby enhancing the healing process of both infected and diabetic wounds. Our study validates that the synergistic integration of photothermal effects, catalytic activity, and released Cu ions can concurrently yield high antibacterial efficiency and tissue regenerative activity, rendering it highly promising for various clinical applications in wound healing.