The SARS-CoV-2 coronavirus (CoV) causes COVID-19, a current global pandemic. SARS-CoV-2 belongs to an order of Nidovirales with very large RNA genomes. It is proposed that the fidelity of CoV genome replication is aided by an RNA nuclease complex, formed of non-structural proteins 14 and 10 (nsp14-nsp10), an attractive target for antiviral inhibition. Here, we confirm that the SARS-CoV-2 nsp14-nsp10 complex is an RNase. Detailed functional characterisation reveals nsp14-nsp10 is a highly versatile nuclease capable of digesting a wide variety of RNA structures, including those with a blocked 3’-terminus. We propose that the role of nsp14-nsp10 in maintaining replication fidelity goes beyond classical proofreading and purges the nascent replicating RNA strand of a range of potentially replication terminating aberrations. Using the developed assays, we identify a series of drug and drug-like molecules that potently inhibit nsp14-nsp10, including the known Sars-Cov-2 major protease (M pro ) inhibitor ebselen and the HIV integrase inhibitor raltegravir, revealing the potential for bifunctional inhibitors in the treatment of COVID-19.