Steric exclusion is a key element of enzyme substrate specificity, including in polymerases. Such substrate specificity restricts the enzymatic synthesis of 2′-modified nucleic acids, which are of interest in nucleic-acid-based drug development. Here we describe the discovery of a two-residue, nascent-strand, steric control ‘gate’ in an archaeal DNA polymerase. We show that engineering of the gate to reduce steric bulk in the context of a previously described RNA polymerase activity unlocks the synthesis of 2′-modified RNA oligomers, specifically the efficient synthesis of both defined and random-sequence 2′-O-methyl-RNA (2′OMe-RNA) and 2′-O-(2-methoxyethyl)-RNA (MOE-RNA) oligomers up to 750 nt. This enabled the discovery of RNA endonuclease catalysts entirely composed of 2′OMe-RNA (2′OMezymes) for the allele-specific cleavage of oncogenic KRAS (G12D) and β-catenin CTNNB1 (S33Y) mRNAs, and the elaboration of mixed 2′OMe-/MOE-RNA aptamers with high affinity for vascular endothelial growth factor. Our results open up these 2′-modified RNAs—used in several approved nucleic acid therapeutics—for enzymatic synthesis and a wider exploration in directed evolution and nanotechnology.