Severe downhole drill-string vibrations can accelerate fatigue damage, leading to substantial economic losses and increased non-productive time. Existing vibration monitoring approaches typically rely on multiple high-cost downhole sensors, which has hindered their widespread deployment in field operations. This work presents a real-time vibration monitoring approach based solely on acceleration measurements and machine-learning techniques. Radial and tangential acceleration signals are generated using a rotor dynamics model and transformed into time–frequency scalograms via continuous wavelet transform. Among various whirl modes, backward whirl is recognized as the most damaging to drilling tools and wellbore integrity. Accordingly, vibration events are classified into backward whirl and non-backward whirl categories, achieving classification accuracies exceeding 94% across different training–testing split ratios. For stick-slip identification, the proposed method distinguishes stick-slip from non-stick-slip conditions with 100% accuracy. Furthermore, based on the stick-slip index, stick-slip vibrations are subdivided into four severity levels—non-stick-slip, low, medium, and high—with classification accuracies exceeding 95% across all severity classes. The generalization capability of the proposed model is validated using independent acceleration data from ABAQUS simulations and field measurements, demonstrating robust performance beyond the training dataset. Backward whirl and stick-slip are accurately classified using single-point acceleration data alone, without requiring rotational speed measurements or symmetrically distributed accelerometers. This approach reduces sensor requirements, lowers operational costs, and facilitates practical real-time deployment.