Nonstructural protein 1 (nsp1) is the first viral protein synthesized during coronavirus (CoV) infection and is a key virulence factor that dampens the innate immune response. It restricts cellular gene expression through a combination of inhibiting translation by blocking the mRNA entry channel of the 40S ribosomal subunit and by promoting mRNA degradation. We performed a detailed structure-guided mutational analysis of CoV-2 nsp1 coupled with in vitro and cell-based functional assays, revealing insight into how it coordinates these activities against host but not viral mRNA. We found that residues in the N-terminal and central regions of nsp1 not involved in docking into the 40S mRNA entry channel nonetheless stabilize its association with the ribosome and mRNA, thereby enhancing its restriction of host gene expression. These residues are also critical for the ability of mRNA containing the CoV-2 leader sequence to escape translational repression. Notably, we identify CoV-2 nsp1 mutants that gain the ability to repress translation of viral leader-containing transcripts. These data support a model in which viral mRNA binding functionally alters the association of nsp1 with the ribosome, which has implications for drug targeting and understanding how engineered or emerging mutations in CoV-2 nsp1 could attenuate the virus.