Virtual Reality technology, when integrated with Surgical Digital Twins (SDTs), offers significant potential in medical training and surgical planning. We present SurgTwinVR, a VR application that immerses users within an SDT and enables them to navigate a high-fidelity virtual replica of the surgical environment. SurgTwinVR is the first VR application to utilize a dynamic 3D environment that is a clone of a real surgery, encompassing the entire surgical scene, including the surgeon, anatomy, and instruments. Our system utilizes a SDT with important improvements for real-time rendering and features to showcase the potential benefits of such an application in surgical education.