It is an example of litotes (or something close to it) rather than a double negative.
As some people have disputed the wording, this is from an online ebook version:
You had only to mention her name at afternoon teas for every woman in the room to rise up, and call her — well — NOT blessed.
(Note: the ebook version uses capitals for emphasis, while a printed version uses italics. But they appear to be identical otherwise.)
He is making the point that the other women were saying bad things about her (cursing her). He does this, euphemistically, by referencing and contrasting with a verse from the Bible (Proverbs 31) where a woman is praised by her children:
Her children rise up and call her blessed
He emphasises the fact that she is not well thought of a couple of sentences later when he says "She could be nice .... But that is another story"
The "— well — NOT blessed" bit to me suggests he (the author/narrator) was about to say something like, "call her whore/evil/cursed" but then decides to lighten it by saying "not blessed".