The mood of the poem is twofold. First, the mood is quite sad. The speaker describes an older woman surrounded with the sight and smell of garbage. She is likely to be homeless. The speaker uses striking descriptions, saying the old woman is "wrapped up like garbage" and that she is a "wet brown bag of a woman." What makes the sight even more tragic is the degree of the woman's decline. She used to be the "best looking gal in georgia." So, the overall tone in these lines is tragic and sad. This is a woman who was once beautiful and in a much better situation in life.
The second part of the twofold mood(s) is hope. Even though this old woman has been destroyed by life, she perseveres. The speaker embraces this idea of hope at the end of the poem. She repeats the phrase "I stand up" to emphasize her support for this woman and others like her. The fact that society has cast this old woman aside makes the speaker want to stand up for her all the more. So, the mood of the poem begins with tragedy and ends with hope.
We do not know the mood of the subject of the poem, Miss Rosie herself. Given the descriptions of her as an old, homeless woman, we can speculate that she is sad and beaten down by life. On the other hand, she might be hopeful because in spite of her poor situation, she is persevering.