The present paper details the complete stereoselective synthesis of four natural acetogenins, chatenaytrienins-1, -2, -3 and -4, previously isolated from the roots of fruit trees of the family Annonaceae (A. nutans and A. muricata), as an inseparable mixture. The novel organometallic reactions, developed by the authors, of Ti-catalyzed cross-cyclomagnesiation of O-containing and aliphatic allenes using available Grignard reagents were applied at the key stage of synthesis. We have studied the biological activity of the synthesized individual chatenaytrienins-1, -2, -3 and -4 in vitro, including their cytotoxicity in a panel of tumor lines and their ability to induce apoptosis, affect the cell cycle and mitochondria, and activate the main apoptotic signaling pathways in the cell, applying modern approaches of flow cytometry and multiplex analysis with Luminex xMAP technology. It has been shown that chatenaytrienins affect mitochondria by uncoupling the processes of mitochondrial respiration, causing the accumulation of ROS ions, followed by the initiation of apoptosis. The most likely mechanism for the death of cortical neurons from the consumption of tea from the seeds of Annona fruit is long-term chronic hypoxia, which leads to the development of an atypical form of Parkinson’s disease that is characteristic of the indigenous inhabitants of Guam and New Caledonia.