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Smart manufacturing becomes a major trend of manufacturing industry in the context of Industry 4.0. The integration of physical manufacturing machines and digitized virtual counterparts is promoted by emerging concepts and technologies of Digital Twin. Aiming to seamlessly integrate the cyberspace and physical world by constructing a bi-directional mapping system, Digital Twin can highly improve the user experience and production efficiency in smart manufacturing. So far little attention has been paid to the mapping from the cyberspace to the physical world in Digital Twin. Without this mapping, operations on the digitized virtual machines are incapable of working on the physical ones, which actually limits the applicability of Digital Twin to more manufacturing processes. In addition, the traditional 2D interactive interface in the cyberspace is limited in visualizing the large amount of digital data and providing concise information to improve the operation efficiency. To optimize the conventional Digital Twin mapping system, this paper proposes a modular-based Digital Twin system for smart manufacturing, where the bi-directional real-time mapping of the cyber–physical space is established through socket communication. Moreover, the proposed Digital Twin system aggregates the functions of remote control and virtual machining using virtual reality and augmented reality. These two essential functions are designed to provide an immersive and friendly operating environment as well as a vivid preview of machining outcomes to improve production efficiency, minimize machining cost, and avoid potential risks. The feasibility and effectiveness of the proposed Digital Twin system are demonstrated by implementing the system on a CNC milling machine where the control latency and virtual machining accuracy are verified. The proposed Digital Twin system can be utilized as an essential part of smart manufacturing, having high potential to be applied to various industrial machines and smart systems.