Team Logo. The Greenville Braves were a team in the Southern League. They were the AA affiliate of the Atlanta Braves. In 2005 they moved and became the Mississippi Braves. Retrieved from "https://prosportsteams.fandom.com/wiki/Greenville_Braves?oldid=7731" Categories: Former SL Teams Teams in South Carolina Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.