The Ducks announced the deals Wednesday.
Hackett has played in 26 NHL games with Minnesota and Buffalo, winning four times. He played for Buffalo and its AHL affiliate in Rochester last season.
Mueller has 10 points in 53 career NHL games with Nashville, Dallas and the New York Rangers. He spent most of last season with the Rangers' AHL affiliate in Hartford.
Piskula has appeared in 13 NHL games with Nashville, Calgary and Los Angeles. He spent most of last season with the Predators' AHL affiliate in Milwaukee.