Cysteine proteases (bromelain, ficin, and papain) are widely used in biotechnology and medicine, but their application is limited by rapid autolysis and oxidative inactivation. This study aimed to develop effective supports for these enzymes based on graft copolymers of sodium alginate and poly(N-vinylpyrrolidone) (SA-g-PVP) and to elucidate the structure–property relationships governing immobilization efficiency, catalytic activity, and storage stability. Copolymers were synthesized via radical solution polymerization under optimized conditions. Enzymes were immobilized by physical adsorption, and the resulting complexes were characterized by Fourier-transform infrared (FTIR) spectroscopy, protein content assays, proteolytic and amidase activity measurements, and molecular docking. The graft copolymer with a smaller particle size in solution provided a larger accessible surface area, leading to higher bromelain and papain loading. Ficin showed the opposite trend due to its unique surface amino acid composition. Immobilization dramatically increased storage stability: half-life values for bromelain, ficin, and papain reached up to 20, 14, and 14 days, respectively, compared to 1–3 days for the free enzymes. Molecular docking revealed that the dense polymer shell stabilizes the enzyme tertiary structure by forming multiple contacts with internal cavities and tunnels, thereby preventing autolysis and conformational unfolding. Collectively, these findings demonstrate that SA-g-PVP copolymers are promising, non-toxic supports for cysteine proteases, with ficin showing up to 100% activity recovery, making them suitable for food, cosmetic, and biomedical applications.