Papillary thyroid carcinoma (PTC) is the most frequent form of thyroid cancer. PTC commonly presents with mutations of the serine/threonine kinase BRAF (BRAFV600E), which drive ERK1/2 pathway activation to support growth and suppress apoptosis. PTC patients often undergo surgical resection; however, since the average age of PTC patients is under 50, adverse effects associated with prolonged maintenance therapy following total thyroidectomy are a concern. The development of mutant-selective BRAF inhibitors (BRAFi), like vemurafenib, has been efficacious in patients with metastatic melanoma, but the response rate is low for mutant BRAF PTC patients. Here, we assay the therapeutic response of BRAFi in a panel of human PTC cell lines and freshly biopsied patient samples. We observed heterogeneous responses to BRAFi, and multi-omic comparisons between susceptible and resistant mutant BRAF PTC revealed overrepresented stress response pathways and the absence of compensatory RTK activation – features that may underpin innate resistance. Importantly, resistant cell lines and patient samples had increased hallmarks of failed apoptosis; a cellular state defined by sublethal caspase activation and DNA damage. Further analysis suggests that the failed apoptotic phenotypes may have features of “minority mitochondrial outer membrane permeabilization (MOMP)” – a stress-related response characterized by fragmented and porous mitochondria known to contribute to cancer aggressiveness. We found that cells presenting with minority MOMP-like phenotypes are dependent on the apoptotic regulator, Mcl-1, as treatment with the Mcl-1 inhibitor, AZD5991, potently induced cell death in resistant cells. Furthermore, PI3K/AKT inhibitors sensitized resistant cells to BRAFi; an effect that was at least in part associated with reduced Mcl-1 levels. Together, these data implicate minority MOMP as a mechanism associated with intrinsic drug resistance and underscore the benefits of targeting Mcl-1 in mutant BRAF PTC.