The Falcons announced the moves Wednesday.
An ankle injury slowed Graf's bid to make the team. He was on Atlanta's practice squad last season.
The Falcons could keep Austin Pasztor as the third tackle even though he has a pectoral injury and won't play in Thursday night's final preseason game against Jacksonville. Pasztor could be cleared for team activities next week.
Davis was an undrafted rookie from Texas Tech. Reggie Davis of Georgia, another undrafted rookie receiver, is still competing for a roster spot.