Toni Cade Bambara's short story "Blues Ain't No Mockingbird" does an effective job of portraying the fact that those who are better off have a tendency to mock and oppress those who are worse off. But more importantly, it also does an effective job of portraying the strength of character and pride that even those who are poor can still have, just like Granny and Granddaddy.
In the short story, the two men filming the family as the children play and Granny makes Christmas cakes claim that they are making a film for the county for the "food stamp campaign" (p. 954). However, what's interesting is that they refer to Granny as "aunty," which as a study guide informs us in footnote 1, was actually "a derogatory term of address once commonly used for black women in the South" (p. 954). Hence, whatever the two camera men are doing, it's certainly not out of respect for the family or others like them in need. They further hint at exactly which side of the food stamp campaign they stand on when they note that Granny grows her own vegetables and that "if more folks did that, see, there's be no need--" What he is starting to say here that is cut short by Granny's silent stare is that there would be no need for food stamps at all. Hence, the two men are certainly not filming the family out of benevolence; instead, they're trying to prove the family is not in need and that there is no need for the county to start spending tax payers' money to distribute food stamps to the poor.
However, Granny is certainly not the type of disadvantaged person who stands by and takes abuse. Instead, she is characterized as strong, full of beneficial pride, and able to tell right from wrong. She portrays her strength of character by running the men off her property and relating a story to the children of a man she once witnessed taking pictures of another suffering man who was about to commit suicide. The moral of the story is that a person's suffering, or a person's "blues," are not something to be "mocked," as is implied by the title.