Team officials confirmed the cuts Tuesday night, hours after head coach Sean Payton had met with reporters. Payton had not indicated that any roster moves were planned.
Mehlhaff, who the Saints drafted last spring but cut after training camp, was brought back to replace injured kicker Martin Gramatica in Week 6. In three games since, Mehlhaff was 3-of-4 on field goals and 9-of-10 on extra points.
He missed an extra point in last Sunday's 37-32 victory in London over the San Diego Chargers.
Carney, now 44, has been kicking for the New York Giants this season.
Graham replaced Steve Weatherford, who was cut after the Saints' loss to Carolina on Oct. 19. Graham's only appearance for the Saints came last Sunday in London. He punted three times, averaging 42 yards.
Weatherford, who was signed by Kansas City last week, was the Saints' only punter from the beginning of the 2006 season, when he was a rookie, until he was cut less than two weeks ago.