Single-nucleotide variants (SNVs) are extremely prevalent in human cancers, although most of these remain clinically unactionable. The programmable RNA nuclease CRISPR-Cas13 has been deployed to specifically target oncogenic RNAs. However, silencing oncogenic SNVs with single-base precision remains extremely challenging due to the intrinsic mismatch tolerance of Cas13. Here, we show that introducing synthetic mismatches at precise positions of the spacer sequence enables de novo design of guide RNAs [CRISPR RNAs (crRNAs)] with strong preferential silencing of point-mutated transcripts. We applied these design principles to effectively silence the oncogenic KRAS G12 hotspot, NRAS G12D and BRAF V600E transcripts with minimal off-target silencing of the wild-type transcripts, underscoring the adaptability of this platform to silence various SNVs. Unexpectedly, the SNV-selective crRNAs harboring mismatched nucleotides reduce the promiscuous collateral activity of the RfxCas13d ortholog. These findings demonstrate that the CRISPR-Cas13 system can be reprogrammed to target mutant transcripts with single-base precision, showcasing the tremendous potential of this tool in personalized transcriptome editing.