We herein report a method for the chemical depolymerization of the epoxy resin present in a carbon composite through an advanced oxidation reaction using hydroxyl radicals. It was found that decomposition of the epoxy resin by the hydroxyl radicals generated from NaOCl was complete within 2 h at 100 °C and ambient pressure in an aqueous solution. The effects of different radical initiators (i.e., potassium persulfate (KPS) and 4,4′-azobis(4-cyanovaleric acid) (ACVA)) on the acceleration of hydroxyl radical generation from NaOCl were also evaluated. More specifically, the rate of hydroxyl radical formation in the presence and absence of a radical initiator was determined using the 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical method, and it was confirmed that the radical generation rate was increased by up to 3 times when the KPS radical initiator was employed (c.f., in the absence of an initiator). Interestingly, it was confirmed that the reaction rate constant (k) increased by up to 5.3 times when the combination of NaOCl and radical initiator KPS was applied to the recycling of carbon fiber-reinforced plastic (CFRP). In addition, X-ray photoelectron spectroscopy, Raman spectroscopy, and Field-emission scanning electron microscopy observations of the reclaimed carbon fiber demonstrated that no significant damage occurred during the reaction. This result is expected to lead to novel methods for enhancing the rate of CFRP chemical recycling processes.