The application of carbon fiber-reinforced composites (CFRCs) is limited owing to the difficulty of chemically recycling carbon fibers (CFs). To address this problem, we cured tung oil-based triglycidyl ester (TOTGE) with menthane diamine (MDA) in order to obtain a chemically degradable bio-based vitrimer matrix. The obtained vitrimer matrix could undergo a dynamic transesterification reaction catalyzed by the tertiary amines generated from the curing reaction. The TOTGE−MDA vitrimer matrix shows excellent self-healing performance, physical reprocessing, and shape memory properties. Meanwhile, CFRCs based on the TOTGE−MDA vitrimer matrix also exhibited excellent reprocessing, self-adhesive, and shape memory properties. The CFRC underwent rapid chemical degradation with ethanolamine at 90 °C. The performance of the recycled CFs was similar to that of the virgin CFs. This work provides an effective solution to facilitate the sustainable development of CFRCs.