Activation of the ubiquitin ligase APC/C by the protein Cdc20 is an essential requirement for proper cell division in higher organisms, including humans. APC/C is the ultimate effector of the Spindle Assembly Checkpoint (SAC), the signalling system that monitors the proper attachment of chromosomes to microtubules during cell division. Defects in this process result in genome instability and cancer. Interfering with APC/C substrate ubiquitylation in cancer cells delays mitotic exit, which induces cell death. Therefore, impairing APC/C function represents an opportunity for the treatment of cancer and malignancies associated with SAC dysregulation. In this study, we report a new class of pyrimidinethylcarbamate apcin analogues that interfere with APC/C activity in 2D and 3D breast cancer cells. The new pyrimidinethylcarbamate apcin analogues exhibited higher cytotoxicity than apcin in all breast cancer cell subtypes investigated, with much lower cytotoxicity observed in fibroblasts and RPE-1 cells. Further molecular rationalisation of apcin and its derivatives was conducted using molecular docking studies. These structural modifications selected from the in silico studies provide a rational basis for the development of more potent chemotypes to treat highly aggressive breast cancer and possibly other aggressive tumour types of diverse tissue origins.