SARS-CoV-2, the agent of the COVID-19 pandemic, can infect a wide range of mammals. Since its spread in humans, secondary host jumps of SARS-CoV-2 from humans to a variety of domestic and wild populations of mammals have been documented. The evolution of SARS-CoV-2 in different host species is of fundamental interest while also providing indication of how SARS-CoV-2 may have adapted to human hosts soon after the initial host jump, a time window for which there are no genome sequences available. Moreover, the study of SARS-CoV-2 circulating in animals is critical to assess the risk that the transmission of animal-adapted viral lineages back into humans (i.e., spillback) may pose. Here, we compared the genomic landscapes of SARS-CoV-2 isolated from animal species relative to that in humans, profiling the mutational biases indicative of potentially different selective pressures in animals. We focused on viral genomes collected in infected mink (Neovison vison) and white-tailed deer (Odocoileus virginianus) for which reports of multiple independent spillover events and subsequent animal-to-animal transmission are available. We identified six candidate mutations for animal-specific adaptation in mink (NSP9_G37E, Spike_F486L, Spike_N501T, Spike_Y453F, ORF3a_T229I, ORF3a_L219V), and one in deer (NSP3a_L1035F), though these mutations appear to confer minimal advantage for circulation in humans. Additionally, circulation of SARS-CoV-2 in mink and deer has not caused considerable changes to the evolutionary trajectory of SARS-CoV-2 thus far. Finally, our results suggest that minimal adaptation was required for human-to-animal spillover and subsequent onward transmission in mink and deer, highlighting the ‘generalist’ nature of SARS-CoV-2 as a pathogen of mammalian hosts.