A digital twin (DT) is an effective means of achieving physical and information fusion and has great potential for achieving a new paradigm of cutting process (CP) intelligence. This paper traces the relevant studies of digital technology in manufacturing and proposes a bionic digital brain (BDB) as the intelligent core of a digital twin-cutting process (DTCP) framework. The BDB was built with digital neurons (DN) as the basic functional unit, and the reaction mechanism between the DN stimulated the BDB to compute intelligently in real time (RT). The left brain obtains the prophetic theoretical processing information through the DN. The right brain receives actual perceptive processing information through the DN. After the corpus callosum fuses the left and right brain information, the DN outputs the optimal control solutions in RT to ensure demand. The details of monitoring, predicting, optimizing, and controlling the CP based on this framework are described in detail through a case study, demonstrating the powerful information processing capability of the BDB and the RT precision intelligent machining effects. The developed DTCP system confirmed the feasibility and effectiveness of the proposed framework. It provided a theoretical and technical reference for applying and promoting DT technology in the CP.