Hemp seed (Cannabis sativa L.) oil comprises a variety of beneficial unsaturated triglycerides with well-documented nutritional and health benefits. However, it can become rancid over a relatively short time period, leading to increased industrial costs and waste of a valuable product. The development of sustainable polymers is presented as a strategy, where both the presence of unsaturation and peroxide content could be effectively used to alleviate both the waste and financial burden. After the reaction with peroxyacetic acid, the incorporation of halloysite nanotubes (HNTs), and the subsequent thermal curing, without the need for organic solvents or interfacial modifiers, flexible transparent materials with a low glass-transition temperature were developed. The improvement in the thermal stability and both the static and dynamic mechanical properties of the bionanocomposites were significantly enhanced with the well-dispersed HNT filler. At an optimum concentration of 0.5 wt % HNTs, a simultaneous increase in stiffness, strength, ductility, and toughness was observed in comparison to the unfilled cured resin. These sustainable food-waste-derived bionanocomposites may provide an interesting alternative to petroleum-based materials, particularly for low-load-bearing applications, such as packaging.