The replication complex (RC) of SARS-CoV-2 was recently shown to be one of the fastest RNA-dependent RNA polymerases of any known coronavirus. With this rapid elongation, the RC is more prone to incorporate mismatches during elongation, resulting in a highly variable genomic sequence. Such mutations render the design of viral protein targets difficult, as drugs optimized for a given viral protein sequence can quickly become inefficient as the genomic sequence evolves. Here, we use biochemical experiments to characterize features of RNA template recognition and elongation fidelity of the SARS-CoV-2 RdRp, and the role of the exonuclease, nsp14. Our study highlights the 2'OH group of the RNA ribose as a critical component for RdRp template recognition and elongation. We show that RdRp fidelity is reduced in the presence of the 3' deoxy-terminator nucleotide 3'dATP, which promotes the incorporation of mismatched nucleotides (leading to U:C, U:G, U:U, C:U, and A:C base pairs). We find that the nsp10-nsp14 heterodimer is unable to degrade RNA products lacking free 2'OH or 3'OH ribose groups. Our results suggest the potential use of 3' deoxy-terminator nucleotides in RNA-derived oligonucleotide inhibitors as antivirals against SARS-CoV-2.