I've heard of people like the Inca mummifying relatives and kings, but haven't heard of any north americans doing so
The Aztecs made mummy bundles in which they wrapped the dead in cloth and placed a mask on their face. Annabeth Headrick suggested that the Teotihuacanos did the same thing which may be why we never find their masks in context in the ground.
North America is a big place and highly variable, I know about burials/ treatment of the dead for only a much smaller area- Southern California. In SoCal, the treatment of the dead changed over time, between cremation and burial. I hope a physical anthropologist or burial-specialist archaeologist can come give you a better answer, but still North America is huge.
There is one famous mummy that I am aware of: Spirit Cave Man from Nevada. It is my recollection that his remains were not intentionally mummified a la Egyptian style, but that is not in the brief article here so I could be wrong.