The mechanistic target of rapamycin complex 1 (mTORC1) supports proliferation through parallel induction of key anabolic processes, including protein, lipid, and nucleotide synthesis. We hypothesized that these processes are coupled to maintain anabolic balance in cells with mTORC1 activation, a common event in human cancers. Loss of the tuberous sclerosis complex (TSC) tumor suppressors results in activation of mTORC1 and development of the tumor syndrome TSC. We find that pharmacological inhibitors of guanylate nucleotide synthesis have selective deleterious effects on TSC-deficient cells, including in mouse tumor models. This effect stems from replication stress and DNA damage caused by mTORC1-driven rRNA synthesis, which renders nucleotide pools limiting. These findings reveal a metabolic vulnerability downstream of mTORC1 triggered by anabolic imbalance.