In this study, model order reduction of high-fidelity off-road mobility models is explored to address the computational intensity of nonlinear finite element deformable tire–soil interaction models. To this end, a model order reduction procedure for the tire–soil interaction model is developed with the proper orthogonal decomposition (POD), and it is integrated into the off-road mobility simulation framework, leveraging high-performance computing. The POD is, however, limited in that the modes are dependent on snapshot data collected during the running of a full order model, limiting the modes to being accurate only for the specific scenario from which they were collected. Due to this limitation, a method of mode adaptation through interpolation on a tangent space of the Grassmann manifold is investigated to allow modes to be predicted for cases in which a full order model has not been run. It is demonstrated by several numerical examples that the POD modes are effective at retaining predictive accuracy while reducing computational time. The results show that adapted POD modes are more capable of characterizing the behavior of the model than modes produced at a different value of the simulation parameter. The POD-based reduced order modeling approach is further extended to the full vehicle simulation on deformable terrain through the co-simulation coupling algorithm by leveraging the high-performance computing technique.