Background: Human papillomavirus (HPV)-unrelated oropharyngeal squamous cell carcinoma (OPSCC) is a clinically aggressive disease characterized by poor outcomes and limited prognostic biomarkers. The Hippo–YAP pathway has emerged as a key regulator of tumorigenesis in epithelial cancers, although its role in OPSCC remains incompletely defined. Methods: We conducted a retrospective study including 215 patients with HPV-negative OPSCC treated surgically with curative intent. Tissue microarrays were constructed, and immunohistochemical analysis of YAP1 and TAZ expression was performed. Associations with clinicopathological variables, disease-free survival (DFS) and disease-specific survival (DSS) were assessed using univariable and multivariable analyses. Results: Nuclear and cytoplasmic YAP1 expression were detected in 53% and 85.6% of tumors, respectively. Both nuclear and cytoplasmic YAP1 expression were significantly associated with reduced DFS (p = 0.019 and p = 0.004, respectively) and DSS (p = 0.01 and p = 0.006, respectively). Multivariable analysis identified nodal involvement (HR = 1.64, p = 0.023) and nuclear YAP1 expression (HR = 1.65, p = 0.004) as independent predictors of DFS, and advanced tumor stage (HR = 1.57, p = 0.038), nodal involvement (HR = 2.34, p < 0.001), and nuclear YAP1 expression (HR = 1.78, p = 0.002) as independent predictors of DSS. In contrast, nuclear TAZ expression was observed at a lower frequency (14.5%) and showed no significant association with clinical parameters or survival outcomes. Conclusions: YAP1 expression, particularly its nuclear activated form, emerges as an independent poor prognostic factor in HPV-negative OPSCC, whereas nuclear TAZ expression was rather infrequent and showed no clinical relevance. These findings highlight the importance of Hippo pathway dysregulation in this tumor subtype and suggest the potential of YAP1 as both a prognostic biomarker and a therapeutic target.