Lytic infection with the two human gammaherpesviruses, Kaposi's sarcoma-associated herpesvirus (KSHV) and Epstein-Barr virus (EBV), leads to significant depletion of the cellular transcriptome. This host shutoff phenotype is driven by the conserved herpesviral alkaline exonuclease, termed SOX in KSHV and BGLF5 in EBV, which in gammaherpesviruses has evolved the genetically separable ability to target cellular mRNA. We now show that host shutoff is also a prominent consequence of murine gammaherpesvirus 68 (MHV68) infection, which is widely used as a model system to study pathogenesis of these viruses in vivo. The effector of MHV68-induced host shutoff is its SOX homolog, here termed muSOX. There is remarkable functional conservation of muSOX host shutoff activities with those of KSHV SOX, including the recently described ability of SOX to induce mRNA hyperadenylation in the nucleus as well as cause nuclear relocalization of the poly(A) binding protein. SOX and muSOX localize to both the nucleus and cytoplasm of infected cells. Using spatially restricted variants of these proteins, we go on to demonstrate that all known host shutoff-related activities of SOX and muSOX are orchestrated exclusively from the cytoplasm. These results have important mechanistic implications for how SOX and muSOX target nascent cellular transcripts in the nucleus. Furthermore, our findings establish MHV68 as a new, genetically tractable model to study host shutoff.