Alphaviruses are arthropod-borne viruses (arboviruses) that include a number of important human and animal pathogens. The natural transmission cycle of alphaviruses requires their presence at high concentrations in the blood of amplification hosts for efficient infection of mosquito vectors. The high-titer viremia development implies multiple rounds of infection that proceed in the background of the developing antiviral cell response aimed at blocking virus spread on an organismal level. Therefore, as for many viruses, if not most of them, alphaviruses have evolved mechanisms directed toward downregulating different components of the antiviral cell reaction and increasing viremia to a level sufficient for the next round of transmission. Using Sindbis virus (SIN) as a model, we demonstrated that (i) the replication of wild-type SIN strongly affects major cellular processes, e.g., transcription and translation of mRNAs; (ii) transcriptional and translational shutoffs are distinctly independent events, and their development can be differentially manipulated by creating different mutations in SIN nonstructural protein nsP2; and (iii) inhibition of transcription, but not translation, is a critical mechanism that SIN employs to suppress the expression of cellular viral stress-inducible genes in cells of vertebrate origin. Downregulation of transcription of all of the cellular mRNAs appears to be a very efficient means of reducing the development of an antiviral response. The ability to cause transcriptional shutoff may partially determine SIN host range and replication in particular tissues.