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Microwave-assisted extraction (MAE) of natural antioxidants from food waste (FW) offers an economically appealing waste management strategy. Here, we characterize five single waste streams (apple, coffee, olive, tomato, and potato peel waste) and study the MAE of phenolic acids from select feedstocks and mixtures. This library of materials enables us to unravel the relationship of the FW composition and physical properties with dielectric properties, heating, and extractive yields. For example, the protein, ash, and moisture contents affect dielectric properties the most. Our study unveils the significance of moisture in free and bound states on FW dielectric properties, heating, and target acid yields. The microwaves primarily heat the solvent (dimethylformamide) due to its superior dielectric properties compared to FW (dry and moist, single and mixtures) at ≤ 0.05 solid-to-liquid ratio. High moisture content provides higher phenolic yields at lower temperatures and shorter times due to enhanced heat and mass transfer by the microwaves. We recommend extraction before drying waste streams. Further, our data indicates significant interactions between components of mixed FW that drive 2-3x higher yields than those predicted from a simple additive model from single component results. Our work provides new insights for developing versatile MAE strategies to treat complex mixed FW feedstocks.