Donald Trump is calling for the deportation of millions of immigrants living in the U.S. illegally and for the end of automatic citizenship for children born to foreigners on U.S. soil, adding specifics to the hard-line immigration stance that first helped his Republican presidential campaign take flight.

The positions, outlined Sunday in a television appearance and Mr. Trump’s first campaign policy paper, fill in some policy details to what so far has been a candidacy driven by free-form television appearances and flashy...