Oncogenic gene fusions are key drivers of cancer, yet most remain untargetable by current therapies. Here, we establish CRISPR-PspCas13b as a personalisable platform for systematic silencing of various fusion transcripts. We reveal that recognition and cleavage of the breakpoint sequence by PspCas13b disrupts the fusion transcript, resulting in efficient protein depletion. Short and long-read RNA sequencing reveal that PspCas13b cleavage produces aberrant, translation-incompetent RNA isoforms with internal deletions proximal to the cleavage site. Importantly, we demonstrate that targeting the BCR::ABL1 breakpoint sequence efficiently degrades both canonical and drug-resistant BCR::ABL1 mutants, which are the primary drivers of tyrosine kinase inhibitor (TKI) resistance and relapse in chronic myeloid leukemia (CML). Molecular profiling revealed that PspCas13b impairs BCR::ABL1 tyrosine phosphokinase activity and triggers extensive transcriptomic and proteomic remodelling, ultimately leading to erythroid differentiation and apoptosis in CML cells that are fully resistant to clinical drugs. Beyond BCR::ABL1 mutants, personalised design of PspCas13b effectively silences other undruggable fusions, including RUNX1::RUNX1T1 and EWSR1::FLI1, key drivers in acute myeloid leukemia and in Ewing’s sarcoma, respectively. Collectively, this study establishes a molecular framework for precise and personalizable targeting of otherwise undruggable or drug-resistant oncogenic transcripts.