Right before the quote about Cora I cited above, Munro says that "duty called him to the islands of the West Indies" which connotes the Caribbean, not South America. The word "remotely" suggests that she was part of a mixed-race class (gradations of race and class tended to go hand in hand in the Caribbean.) It is possible that she was of Native American orgins, since thousands of Native Americans were sold from the North American mainland, especially South Carolina, to the Caribbean in the early eighteenth century. But it seems clear that she wasn't South American. I agree that Cooper, through Munro, is pretty ambiguous about the subject, but again, that is very much in keeping with the themes of ambiguous lineage throughout the book.
Cora's mother was the daughter of a West Indies plantation owner and a woman of mixed ancestry. As Munro euphemistically puts it:
She was a daughter of a gentleman of those isles by a lady whose misfortune it was, if you will...to be descended, remotely, from that unfortunate class who are so basely enslaved to administer to the wants of a luxurious people.
Unlike the American South, where the children of white men and black women were usually themselves enslaved, West Indian society was considerably less binary in terms of race, a consequence of the very high proportion of Africans to whites. So neither Cora's mother nor her grandmother seem to have been (nor, historically, would they probably have been) slaves.
The racial distinction, however, is significant in Cooper's story, as Cora, often described in racialized terms, displays a boldness that was not typically associated with Euro-American women. She is contrasted with her meek, demure sister Alice, who is the daughter of a British woman.
Heredity, race, and culture (and the ambiguities therein) are themes that permeate The Last of the Mohicans. The title of the book is a reference to the fact that Uncas was supposed to succeed his father as the last sagamore of the Mohicans. It is also present in Nathaniel, who frequently points out that as a white man, he is civilized, despite his Indian upbringing.