During the construction of mountain tunnels, there are often various intricate and mutable potential hazards, the management and control of which are crucial to ensuring the safety of such construction. With the rapid advancement of engineering information technologies, including Building Information Model (BIM), the internet, big data, and cloud computing, dynamic management of mountain tunnel construction will inevitably become a prevailing trend. This paper proposes a new digital approach to realize the informatization and visualization of risk management in mountain tunnel construction, by combining monitoring measurement with advanced geological prediction based on BIM technology. The proposed approach suggests a BIM-based digital platform architecture for mountain tunnel construction, which is comprised of five layers—basic, model, data, application, and user. The integration of these five layers can realize risk management information during the construction of mountain tunnels. In addition, a set of dynamic risk management systems, including risk monitoring, identification, and assessment, can be established based on the digital platform. The digital platform and dynamic risk management system proposed in this paper have certain advantages in the construction of mountain tunnels, providing a new and significant way for the management of safety risks in such construction projects.