Chronic wounds incidence is increasing and affects millions of people around the world, causing great psychological and socio-economic impacts. However, treatments that can effectively promote wound healing are still lacking. In this study, grape pomace (GP), the main residue from winemaking production was explored as a source of high added-value raw material directed for the topical treatment of Staphylococcus aureus chronic wound infections. Crude GP extracts (composed of stalks or a skin and seeds mixture–from red and white grape varieties) obtained using a modified solid-liquid extraction (water, ethanol, and acetone solvents) were evaluated for their antioxidant capacity (ABTS and DPPH assays), as well as the richness of phenolic compounds (total phenolic content-TPC, total flavonoid content-TFC, and HPLC-DAD assays). The GP extracts with the most favorable results were incorporated in a chitosan-alginate hydrogel (cross-linked with glutaraldehyde and calcium chloride), characterized (swelling, degradation, and release properties), and tested for its bioactivity (antioxidant and antimicrobial potential). TPC and TFC were higher in red GP extracts, as confirmed by the HPLC analysis, indicating a greater diversity of compounds in these extracts. Ethanolic white GP extracts (from skin-seeds mixture) showed the highest extraction yield and antioxidant activity. Their incorporation into the chitosan-alginate hydrogel improved its swelling and antimicrobial properties (total cytoplasmic membranes disruption and culturability reduction). A biomaterial with high swelling capacity and antibacterial activity against S. aureus was obtained, which can potentially promote wound healing by exudate absorption and infection clearance while promoting valorization of by-products and stimulating a circular economy.