There's a lot, lot, lot more to it than simply saying that it's a DNA vs an RNA virus and that one categorically mutates faster than the other. The most relevant factor here is that COVID-19 only has a single strand of RNA, whereas e.g. influenza has 8. This allows a lot more mutation from pieces of RNA swapping around between different strands, which just can't happen on COVID-19. You can sort of think of it as analogous to sexual vs asexual reproduction; the former has a lot more potential for variation. Plus there's factors relating to the specific mechanism that coronaviruses use to attach to animal cells that make them less capable of mutating into any sort of a different shape that's still effective at all.

And I'm nothing close to an expert on any of this. But refer to sources, e.g.:

https://www.businessinsider.com/new-coronavirus-mutates-slow...

https://www.washingtonpost.com/health/the-coronavirus-isnt-m...