We explored the effect of a new resveratrol (RVT) derivative, 3,3′,4,4′-tetrahydroxy-trans-stilbene (3,3′,4,4′-THS), on viability, apoptosis, proliferation, and senescence of three representative lines of ovarian cancer cells, that is, A2780, OVCAR-3, and SKOV-3,in vitro. In addition, the mechanistic aspects of 3,3′,4,4′-THS activity, including cell redox homeostasis (the production of reactive oxygen species, activity of enzymatic antioxidants, and magnitude of DNA damage accumulation and repair), and the activity of caspases (3, 8, and 9) and p38 MAPK were examined. The study showed that 3,3′,4,4′-THS affects cancer cell viability much more efficiently than its parent drug. This effect coincided with increased generation of reactive oxygen species, downregulated activity of superoxide dismutase and catalase, and excessive accumulation of 8-hydroxy-2′-deoxyguanosine and its insufficient repair due to decreased expression of DNA glycosylase I. Cytotoxicity elicited by 3,3′,4,4′-THS was related to increased incidence of apoptosis, which was mediated by caspases 3 and 9. Moreover, 3,3′,4,4′-THS inhibited cancer cell proliferation and accelerated senescence, which was accompanied by the activation of p38 MAPK. Collectively, our findings indicate that 3,3′,4,4′-THS may constitute a valuable tool in the fight against ovarian malignancy and that the anticancer capabilities of this stilbene proceed in an oxidative stress-dependent mechanism.