In this study, soy protein isolate (SPI) films incorporating quercetin-grafted dialdehyde starch (DAS-QR) and DAS/QR, respectively, were developed. The structural, physical, and functional properties of the composite films were determined. The results suggested that DAS-QR and DAS/QR formed hydrogen bonding with the SPI matrix, which improved the structural properties of the films. The light-blocking capacity, thermal stability, hydrophobicity, tensile strength, elongation at break, and antioxidant and antibacterial abilities of SPI films were improved by DAS-QR and DAS/QR. Notably, SPI films incorporated with DAS-QR exhibited better performance than those with DAS/QR in terms of antioxidant (SPI/DAS-QR: 79.8% of DPPH and 62.1% of ABTS scavenging activity; SPI/DAS/QR: 71.4% of DPPH and 56.0% of ABTS scavenging activity) and antibacterial abilities against S. aureus (inhibition rate: 92.7% for SPI/DAS-QR, 83.4% for SPI/DAS/QR). The composite coating film SPI/DAS-QR effectively maintained appearance quality, delayed the loss of weight and total soluble solids, postponed malondialdehyde accumulation, and decreased peroxidase activity and microbial contamination in fresh-cut potatoes. These good performances highlight SPI/DAS-QR as a promising active packaging material for fresh-cut product preservation.