Homeostatic mechanisms can eliminate abnormal cells to prevent diseases such as cancer. However, the underlying mechanisms of this surveillance are poorly understood. Here we investigated how clones of cells mutant for the neoplastic tumor suppressor gene scribble (scrib) are eliminated from Drosophila imaginal discs. When all cells in imaginal discs are mutant for scrib, they hyperactivate the Hippo pathway effector Yorkie (Yki), which drives growth of the discs into large neoplastic masses. Strikingly, when discs also contain normal cells, the scrib(-) cells do not overproliferate and eventually undergo apoptosis through JNK-dependent mechanisms. However, induction of apoptosis does not explain how scrib(-) cells are prevented from overproliferating. We report that cell competition between scrib(-) and wild-type cells prevents hyperproliferation by suppressing Yki activity in scrib(-) cells. Suppressing Yki activation is critical for scrib(-) clone elimination by cell competition, and experimental elevation of Yki activity in scrib(-) cells is sufficient to fuel their neoplastic growth. Thus, cell competition acts as a tumor-suppressing mechanism by regulating the Hippo pathway in scrib(-) cells.