Background on this question: CRISPR-Cas is a naturally occurring process in bacteria that is used to adapt to viral attacks. We've coopted the system for use in mammals.
As far as I know a few labs in this space are operating under the basic question, "why haven't viruses killed everything by now?"
So this category of research is more or less the answer.
> Do mammals have a CRISPR analog?
Not exactly. There are things like https://en.wikipedia.org/wiki/Ribonuclease_L that nuke cells and are stimulated by interferons. This might be why interferon injections are common chronic therapeutics for diseases in this space.
The closest thing we have is probably whatever adaptability B or T cells can muster on their own? I'm sure someone lurking in the comments has a better answer.