With the aim to fully exploit the by-products obtained after the industrial extraction of starch from sweet potatoes, a cascading approach was developed to extract high-value molecules, such as proteins and pectins, and to valorize the solid fraction, rich in starch and fibrous components. This fraction was used to prepare new biocomposites designed for food packaging applications. The sweet potato residue was added to poly(3-hydroxybutyrate-co-3-hydroxyvalerate) in various amounts up to 40 wt % by melt mixing, without any previous treatment. The composites are semicrystalline materials, characterized by thermal stability up to 260 °C. For the composites containing up to 10 wt % of residue, the tensile strength remains over 30 MPa and the strain stays over 3.2%. A homogeneous dispersion of the sweet potato waste into the bio-polymeric matrix was achieved but, despite the presence of hydrogen bond interactions between the components, a poor interfacial adhesion was detected. Considering the significant percentage of sweet potato waste used, the biocomposites obtained show a low economic and environmental impact, resulting in an interesting bio-alternative to the materials commonly used in the packaging industry. Thus, according to the principles of a circular economy, the preparation of the biocomposites closes the loop of the complete valorization of sweet potato products and by-products.