I don’t think elephants can live for long enough at the North Pole to be able to have children, so I’m not sure they would be able to adapt to their environment by evolution.
But if you started moving elephants north, to places that were slightly colder, after a long enough time and enough generations they should be able to adapt to that. Then you could move them further north again, and they would get used to even colder temperatures. Eventually (and this would take a very long time) you would be able to evolve a species of elephant that could live at the north pole. Presumably these would look quite a lot like mammoths.
Elephants wouldn’t survive at the north pole without changing the environment a lot. That would mean it would evolve into the adapted environment. Also it wouldn’t evolve into a mammoth, it would change into something else most likely. It might be very mammoth like, but would be slightly different.