Plants from the Bursera genus are widely distributed in the tropical dry forests of Mexico. In traditional medicine, extracts from different species of Bursera have been used for a wide range of biological activities, including the treatment of cancer-related symptoms. Compounds present in the Bursera genus include lignans, flavonoids, steroids, short-chain aliphatic alkanes, acetates, alcohols, ketones, and terpenoids. In some instances, secondary metabolites of these classes of compounds may induce cytotoxicity, and therefore we sought to investigate the effects of B. copallifera leaf extracts in breast cancer cell lines to evaluate their potential therapeutic value for the treatment of breast cancer, one of the most prevalent types of cancer in women worldwide. Two B. copallifera leaf extracts exerted cytotoxic effects on both the MCF7 and MDA-MB-231 breast cancer cell line models. The cytotoxic effect was more evident in the MDA-MB-231 triple negative cell line inhibiting also the migration of these cells. We identified hydroxycinnamic acid and flavonol derivatives as major phenolic components of the extracts. Our results strongly suggest a potential use of the Bursera leaf extracts rich in phenolic compounds, their individual phenolic compounds, or their combinations for the treatment of breast cancer.