Did Sherman exterminate anyone? His idea was to destroy the resources (to the extent that he could) that the other side used to carry on the war. That’s not what WWII’s exterminationist regimes were doing — they went much further. It is what the US has been doing in so many of its wars.
Now you are getting into the finer points of extermination - bad extermination, good extermination, and common-sense extermination.
Any conversation about extermination must include a look at the intent of the people advocating it. Sherman - from his writings - was rather clear what he meant.
I don't have the quotes at my finder tips but if you deny Sherman advocated extermination of his enemies I may have to do a search.