Heasley cleared waivers and was outrighted to Triple-A Durham on Saturday, Marc Topkin of the Tampa Bay Times reports.
Heasley had a brief stint with the big-league club this week, allowing five runs over four innings in an appearance May 27. He was DFA'd on Friday and is now back with Durham. Heasley has a career 6.04 ERA over 143 major-league regular-season innings, so he's likely to serve as bullpen depth for when the big club needs an extra arm.