Sirt6 is involved in multiple biological processes, including aging, metabolism, and tumor suppression. Sirt1, another member of the sirtuin family, functionally overlaps with Sirt6, but its role in tumorigenesis is controversial. In this study, we focused on cell death in association with Sirt6/Sirt1 and reactive oxygen species (ROS) in head and neck squamous cell carcinomas (HNSCCs). Sirt6 induced cell death, as widely reported, but Sirt1 contributed to cell death only when it was suppressed by Sirt6 via regulation of MDM2. Sirt6 and Sirt6-mediated suppression of Sirt1 upregulated ROS, which further led to HNSCC cell death. These results provide insight into the molecular roles of Sirt6 and Sirt1 in tumorigenesis and could therefore contribute to the development of novel strategies to treat HNSCC.