The repair process for oral and maxillofacial injuries involves hemostasis, inflammation, proliferation, and remodeling. Injury repair involves a variety of cells, including platelets, immune cells, fibroblasts, and various cytokines. Rapid and adequate healing of oral and maxillofacial trauma is a major concern to patients. Functional drug-delivery hydrogels play an active role in promoting wound healing and have shown unique advantages in wound dressings. Functional hydrogels promote wound healing through their adhesive, anti-inflammatory, antioxidant, antibacterial, hemostatic, angiogenic, and re-epithelialization-promoting properties, effectively sealing wounds and reducing inflammation. In addition, functional hydrogels can respond to changes in temperature, light, magnetic fields, pH, and reactive oxygen species to release drugs, enabling precise treatment. Furthermore, hydrogels can deliver various cargos that promote healing, including nucleic acids, cytokines, small-molecule drugs, stem cells, exosomes, and nanomaterials. Therefore, functional drug-delivery hydrogels have a positive impact on the healing of oral and maxillofacial injuries. This review describes the oral mucosal structure and healing process and summarizes the currently available responsive hydrogels used to promote wound healing.