Pressure-sensitive adhesives typically used for bandages are nonbiodegradable, inhibiting healing, and may cause an allergic reaction. Here, we investigated the effect of biodegradable copolymers with promising thermomechanical properties on wound healing for their eventual use as biodegradable, biocompatible adhesives. Blends of low molecular weight (LMW) and high molecular weight (HMW) poly(lactide-co-caprolactone) (PLCL) are investigated as tissue adhesives in comparison to a clinical control. Wounds treated with PLCL blend adhesives heal completely with similar vascularization, scarring, and inflammation indicators, yet require fewer dressing changes due to integration of the PLCL adhesive into the wound. A blend of LMW and HMW PLCL produces an adhesive material with significantly higher adhesive strength than either neat polymer. Wound adhesion is comparable to a polyurethane bandage, utilizing conventional nonbiodegradable adhesives designed for extremely strong adhesion.