Nucleic-acid catalysts (ribozymes, DNA- and XNAzymes) cleave target (m)RNAs with high specificity but have shown limited efficacy in clinical applications. Here we report on the in vitro evolution and engineering of a highly specific modular RNA endonuclease XNAzyme, FR6_1, composed of 2'-deoxy-2'-fluoro-β-D-arabino nucleic acid (FANA). FR6_1 overcomes the activity limitations of previous DNA- and XNAzymes and can be retargeted to cleave highly structured full-length (>5 kb) BRAF and KRAS mRNAs at physiological Mg2+ concentrations with allelic selectivity for tumour-associated (BRAF V600E and KRAS G12D) mutations. Phosphorothioate-FANA modification enhances FR6_1 biostability and enables rapid KRAS mRNA knockdown in cultured human adenocarcinoma cells with a G12D-allele-specific component provided by in vivo XNAzyme cleavage activity. These results provide a starting point for the development of improved gene-silencing agents based on FANA or other XNA chemistries.