Head and neck squamous cell carcinoma (HNSCC) includes a subset of cancers driven by human papillomavirus (HPV). Here we use single-cell RNA-seq to profile both HPV-positive and HPV-negative oropharyngeal tumors, uncovering a high level of cellular diversity within and between tumors. First, we detect diverse chromosomal aberrations within individual tumors, suggesting genomic instability and enabling the identification of malignant cells even at pathologically negative margins. Second, we uncover diversity with respect to HNSCC subtypes and other cellular states such as the cell cycle, senescence and epithelial-mesenchymal transitions. Third, we find heterogeneity in viral gene expression within HPV-positive tumors. HPV expression is lost or repressed in a subset of cells, which are associated with a decrease in HPV-associated cell cycle phenotypes, decreased response to treatment, increased invasion and poor prognosis. These findings suggest that HPV expression diversity must be considered during diagnosis and treatment of HPV-positive tumors, with important prognostic ramifications.