Digital twins (DTs) represent a transformative innovation in healthcare technology, enabling the creation of virtual models that mirror physical systems and processes while supporting real-time simulation, validation, and training. In surgical robotics, this technology holds significant potential to enhance procedural safety, precision, and operational efficiency. This paper presents the design and implementation of a digital twin for a collaborative robotic platform tailored to pedicle screw placement in spinal surgery. The proposed framework establishes a dynamic virtual replica that evolves synchronously with the physical system throughout its lifecycle, ensuring bidirectional adaptation via continuous data integration. To achieve this, we adopt a Model-Based Systems Engineering (MBSE) approach, emphasizing the central role of formalized models to address the complexity of safety-critical systems. Using the Systems Modeling Language (SysML), we develop interconnected models that rigorously define system requirements, architecture, behavior, and constraints. By embedding MBSE into the DT engineering process, this framework provides a structured methodology for robust system design, continuous validation, and operational optimization in surgical robotics.