A new method for the recycling of a polyester tire cord under the action of oligoethylene terephthalates, bis(2-hydroxyethyl) terephthalate and ethylene glycol has been proposed. The method involves simultaneous homogeneous glycolysis of polyethylene terephthalate and devulcanization of crumb rubber. Polyester cord and glycolysates were characterized by FTIR spectroscopy and gel permeation chromatography (GPC). The devulcanization process was investigated by swelling-based methods. The rate of the proposed method of homogeneous glycolysis in a melt phase was proved to be higher than one of the heterogeneous glycolysis. The assumption of a more efficient devulcanization in the presence of a softener was also confirmed. The degree of devulcanization 46.07%, the apparent degree of swelling 167.4%, and the apparent swelling rate constant 0.0902 min−1 were achieved. The results indicate that the proposed method made it possible to carry out the glycolysis of the polyester cord of the tire more deeply than the known heterogeneous glycolysis with various agents, but further research is needed for industrial implementation.