To enable the recycling of carbon fiber composites, this study developed a resveratrol-based epoxy vitrimer containing double dynamic covalent bonds (ester and disulfide bonds) by using bio-based polyphenolic resveratrol epoxy resin (RE), with dynamic disulfide-containing lipoic acid (LA) as a crosslinking agent and curing agent phthalic anhydride (PA). By adjusting the ratio of the crosslinking agent to the curing agent, the synergistic optimization of the thermal and mechanical properties of the epoxy vitrimer and its composite was achieved. A variety of testing methods were employed to systematically investigate the thermal properties, mechanical properties, and chemical degradation behavior of this epoxy vitrimer. Carbon fiber reinforced composites (CFRCs) based on this epoxy vitrimer were subsequently fabricated. The CFRC reached its optimal mechanical and recycled properties when the resin system had a molar ratio of RE (epoxy): LA (carboxyl): PA (carboxyl) = 5: 1: 4 and the composite resin content was 40% ± 2.7%. Finally, the composite was immersed in a mixed solution of DMF and β-mercaptoethanol (2-ME) (1: 1, v/v), which successfully dissolved the matrix resin and obtained relatively pure carbon fiber.