Coronavirus disease 2019 is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Influential variants and mutants of this virus continue to emerge, and more effective virus-related information is urgently required for identifying and predicting new mutants. According to earlier reports, synonymous substitutions were considered phenotypically silent; thus, such mutations were frequently ignored in studies of viral mutations because they did not directly cause amino acid changes. However, recent studies have shown that synonymous substitutions are not completely silent, and their patterns and potential functional correlations should thus be delineated for better control of the pandemic. In this study, we estimated the synonymous evolutionary rate (SER) across the SARS-CoV-2 genome and used it to infer the relationship between the viral RNA and host protein. We also assessed the patterns of characteristic mutations found in different viral lineages. We found that the SER varies across the genome and that the variation is primarily influenced by codon-related factors. Moreover, the conserved motifs identified based on the SER were found to be related to host RNA transport and regulation. Importantly, the majority of the existing fixed-characteristic mutations for five important virus lineages (Alpha, Beta, Gamma, Delta, and Omicron) were significantly enriched in partially constrained regions. Taken together, our results provide unique information on the evolutionary and functional dynamics of SARS-CoV-2 based on synonymous mutations and offer potentially useful information for better control of the SARS-CoV-2 pandemic.