Chronic pain (CP) affects over 30% of the global population and is the leading cause of disability worldwide. Diagnosing and managing CP remains challenging due to overlapping pain mechanisms, i.e., nociceptive, neuropathic, and nociplastic, which frequently coexist within individual patients. This study introduces a novel, data-driven machine learning pipeline that integrates autoencoder-based feature extraction with Fuzzy C-Means clustering to identify, quantify, and interpret coexisting CP mechanisms using patient-reported data. Two retrospective datasets from tertiary pain clinics were analyzed (DADOS: 451 patients, 44 features; TRIC: 195 patients, 28 features), encompassing mixed-type clinical, psychosocial, and behavioral parameters. The proposed model achieved a Hamming loss of 0.43 in multi-label classification, outperforming both unsupervised (k-prototypes) and semi-supervised baselines; empirically validating the hypothesis that CP exists on a mechanistic continuum rather than as discrete categories. Compared with existing clustering studies that focus on single pain disorders or neglect overlapping mechanisms, our approach provides quantitative estimates of mechanistic dominance for each patient, enabling personalized, mechanism-based treatment decisions without reliance on imaging or invasive procedures. This work highlights the timeliness and clinical significance of computational approaches in CP research, offering a scalable, interpretable, and resource-efficient framework for advancing mechanism-based diagnosis and management.