Cunniff was optioned to Triple-A Gwinnett on Tuesday.
The Braves made a flurry of roster moves Tuesday, bringing up John Gant and Shae Simmons to bolster the bullpen. With that, Cunniff was the roster casualty after serving up four earned runs while only recording one out in his most recent appearance. He'll likely continue to work out of the bullpen at Gwinnett, but he could rejoin the Braves after rosters expand later in the week.