Donald Trump blasted Hillary Clinton in an economic-policy speech that sought to pick off some of her supporters, while the Democratic presidential nominee dismissed her rival’s plans as a repackaging of old Republican ideas.

In an appearance before the Detroit Economic Club on Monday, Mr. Trump fused his populist message with appeals designed to win support from the left—such as defraying households’ child-care costs—alongside a full embrace of policies on regulation, corporate taxes and energy production to try to please...