Manually grading structural changes with the modified Stoke Ankylosing Spondylitis Spinal Score (mSASSS) on spinal X-ray imaging is costly and time-consuming due to bone shape complexity and image quality variations. In this study, we address this challenge by prototyping a 2-step auto-grading pipeline, called VertXGradeNet, to automatically predict mSASSS scores for the cervical and lumbar vertebral units (VUs) in X-ray spinal imaging. The VertXGradeNet utilizes VUs generated by our previously developed VU extraction pipeline (VertXNet) as input and predicts mSASSS based on those VUs. VertXGradeNet was evaluated on an in-house dataset of lateral cervical and lumbar X-ray images for axial spondylarthritis patients. Our results show that VertXGradeNet can predict the mSASSS score for each VU when the data is limited in quantity and imbalanced. Overall, it can achieve a balanced accuracy of 0.56 and 0.51 for 4 different mSASSS scores (i.e., a score of 0, 1, 2, 3) on two test datasets. The accuracy of the presented method shows the potential to streamline the spinal radiograph readings and therefore reduce the cost of future clinical trials.