Alphavirus infections cause multiple alterations in the intracellular environment that can have both positive and negative effects on viral replication. The Old World alphaviruses, such as Sindbis (SINV), chikungunya (CHIKV), and Semliki Forest viruses, hinder the ability of vertebrate cells to form stress granules (SGs). Previously, this inhibitory function was attributed to the hypervariable domain (HVD) of nsP3, which sequesters the key components of SGs, G3BP1 and G3BP2, and to the nsP3 macro domain. The macro domain possesses ADP-ribosylhydrolase activity, which can diminish the ADP-ribosylation of G3BP1 during viral replication. However, our recent findings do not support the prevailing notions. We demonstrate that the interactions between SINV- or CHIKV-specific nsP3s and G3BPs, and the ADP-ribosylhydrolase activity are not major contributors to the inhibitory process, at least when nsP3 is expressed at biologically relevant levels. Instead, the primary factors responsible for suppressing SG formation are virus-induced transcriptional and translational shutoffs that rapidly develop within the first few hours post infection. Poorly replicating SINV variants carrying mutated nsP3 HVD still inhibit SG development even in the presence of NaAs. Conversely, SINV mutants lacking transcription and/or translation inhibitory functions lose their ability to inhibit SGs, despite expressing high levels of wt nsP3. Moreover, we found that stable cell lines expressing GFP-nsP3 fusions retain the capacity to form SGs when exposed to sodium arsenite. However, our results do not rule out a possibility that additional virus-induced changes in cell biology may contribute to the suppression of SG formation.