Carbon fiber (CF)-reinforced thermoset resin matrix composites are widely used in aerospace, national defense, and military due to their outstanding mechanical and thermal properties. The recycling of CFs has social and economic benefits. After curing, the thermoset resin has a three-dimensional cross-linked network structure, making it challenging to balance its mechanical and thermal properties with the degradation and recycling efficiency. The severe recycling conditions can damage CFs. In this study, a new resin system is designed and prepared based on vinylogous urethane vitrimers (VUvs) containing dynamic bonds and bisphenol A-aniline-based benzoxazine (BA-a) with improved mechanical (impact strength up to 16.9 kJ/m2) and thermal properties (higher than 300 °C for Td5) that can be degraded under mild conditions (70 °C, 4 h). Moreover, the monofilament tensile strength of the recovered CF of BA-a/VUv CF-reinforced composites was identical to that of the original CF. Thus, this robust and degradable material system is ideal for the high performance of CF composites and for recycling valuable CFs.