There are of course similarities between the way the Sámi and the Native Americans were treated, but I don’t think they run deep. It mainly comes down to human nature — there have always been people who try to exploit others, everywhere, anytime, with any excuse they can find. So while exploitation may have happened in both cases, the nature of the conflicts were different.
For starters, the Sámi weren’t warriors. Unlike with Native Americans, there were no military conflicts, no peace treaties, and no reservations. Furthermore, in the case of Native Americans, white man was mostly interested in their lands and valuables found there. It wasn’t about ruining their culture as such, it was about material goods. Possibly a few missionaries may have been interested in changing their ways, but they didn’t have much real power over them. So the Native Americans were at least in a position to defend their culture, if not their lands. (Not that this makes it okay, of course. It was still very coldblooded and cruel.)
The Sámi were assaulted in a quite different, and more sophisticated, way. It wasn’t about territory, valuables, or power. It was only about destroying their culture, for various reasons. It may be obvious why the church was interested, but the secular authorities also had their reasons, namely “social darwinism”, the idea that some cultures are superior to others, and that progress happens when inferior ones die — with the implication that actively destroying inferior cultures is both ethically justifiable and a good idea. Since the Sámi people and culture were considered primitive, Norwegians authorities wanted to convert them to Norwegian culture “for their own good”, because, as they saw it, the Sámi culture was bad for the Sámi people. Essentially, destroying their culture was seen as an act of benevolence, of “uplifting” them. It had no other particular purpose, it wasn’t about money or land or anything (although some greedy people took advantage of it, naturally). It was only about people thinking their own culture is superior, and that this made it okay for them to destroy other cultures by any means necessary.
And, with secular authorities on their side, missionaries did have a lot more power in Sámi areas than they might otherwise have had.
In the latter half of the 20th century, Norwegian authorities finally started acknowledging that this was wrong. In 1997, the King of Norway made an official apology. However, Norway is still resisting a full public investigation.