Since its emergence in Wuhan, China in late 2019, the origin and evolution of SARS-CoV-2 have been among the most debated issues related to COVID-19. Throughout its spread around the world, the viral genome continued acquiring new mutations and some of them became widespread. Among them, 14408 C>T and 23403 A>G mutations in RdRp and S, respectively, became dominant in Europe and the US, which led to debates regarding their effects on the mutability and transmissibility of the virus. In this study, we aimed to investigate possible differences between time-dependent variation of mutation densities (MDe) of viral strains that carry these two mutations and those that do not. Our analyses at the genome and gene level led to two important findings: First, time-dependent changes in the average MDe of circulating SARS-CoV-2 genomes showed different characteristics before and after the beginning of April, when daily new case numbers started levelling off. Second, this pattern was much delayed or even non-existent for the "mutant" (MT) strain that harbored both 14408 C>T and 23403 A>G mutations. Although these differences were not limited to a few hotspots, it is intriguing that the MDe increase is most evident in two critical genes, S and Orf1ab, which are also the genes that harbor the defining mutations of the MT genotype. The nature of these unexpected relationships warrants further research.