Background/Objectives: Hepatocellular carcinoma (HCC) is the most common primary liver cancer worldwide, posing significant health challenges due to its high morbidity and mortality rates. Emerging evidence indicates that non-apoptotic cell death mechanisms, including pyroptosis and cuproptosis, play crucial roles in HCC progression. Natural compounds have been widely investigated as potential primary or adjunct therapies targeting these cell death pathways. This review summarizes recent advances on the application of natural products that influence pyroptosis and cuproptosis in HCC. Methods: A comprehensive critical review of in vitro and in vivo studies examining the effects of natural compounds on HCC was conducted. Results: Several natural molecules demonstrate cytotoxic and cytostatic effects against HCC by modulating pyroptosis and cuproptosis pathways. Conclusions: Natural products exhibit promising potential as adjuvant therapies in hepatocellular carcinoma by selectively inducing or modulating pyroptosis and cuproptosis pathways. These mechanisms contribute to enhanced cancer cell death, underscoring the therapeutic value of targeting non-apoptotic cell death processes in HCC management.