How did/do native Americans shave their heads/faces?
First, white men introduced and practiced scalping (look up your facts!). Second, their are several ways for them to shave the limited amount of facial hair they produced anyway including hand-held implements, salves and poultices. Remember, they were able to cope and survive with a number of everyday tasks a long time before the barbaric Europeans came over and slaughtered them and shoved them on arid, unfertile reservations.
First, some Native Americans did not have heavy beards. They had very sharp knives and water, so I am sure they manages their beards and their heads that way. If they knew how to scalp in seconds, they could shave in a few minutes and be more careful I am sure. Before that, very sharp cutting tools like obsidian perhaps which can be sharpened like a blade.