The offshore drilling industry is crucial in extracting oil and gas from deep-sea environments, where the drilling column endures tension, torsion, hydrodynamic forces, among other effects. Assessing its structural integrity and operational efficiency often requires high-fidelity and computationally expensive simulations. This paper proposes a methodology to apply the Dynamic Mode Decomposition (DMD) along with Grassmann manifolds to develop parametric reduced-order surrogate for drill string based on simulated dynamic data. The proposed drill string model accounts for: platform displacement, rotary control at the top drive, waves and current forces, riserless configuration, borehole contact, directional drilling, nonlinear beam axial-lateral-torsional vibrations, and nonlinear axial-torsional bit-rock interaction. Its dynamic response is consistent with field data (torque, force, and bit angular speed). Snapshots of the dynamic response are gathered, a high-order DMD is used, and the most influential modes are selected to preserve the original system's essential dynamics and physical phenomena, significantly reducing computational cost. Several Koopman operators trained on different parameter sets are used, and Grassmann manifolds are employed for parametric interpolation. To validate the approach, all available data will be split into two sets: one for training and the other for validation. The reduced-order model can reconstruct the original signal and predict system behavior beyond the training set, demonstrating faithful representation despite dimensional reduction. The introduction of parametric interpolation is expected to enable the projection of drill-string dynamics using a set of untrained parameters. Results confirm that the proposed DMD strategy is an effective data-driven tool for constructing Reduced Order Models (ROMs) in offshore drilling applications, enabling substantial time savings. Expected results from parametric interpolation should provide a practical, real-time analysis and decision-making pathway for complex offshore operations.