Not 100 percent sure of that answer, but the father (SIMBA?) in the Lion King was the first on-screen death in a Disney film. Bambi's mother was never shown being killed on-screen , as is generally quoted, incidentally.
This question has come up before and the consensus was that it was Davy Crockett (at the Alamo) in Disney's 1955 live action film "Davy Crockett, King of the Wild Frontier".