Kaine agreed, "He hasn't changed one bit."
In August, Trump said during a Fox News town hall that there may be a "softening" of his controversial immigration proposals.
Last week, however, in a speech in Phoenix, Arizona, Trump indicated a commitment to removing undocumented immigrants, saying: "Anyone who has entered the United States illegally is subject to deportation."
Clinton said the seeming flip-flop was indicative of the "kind of games that [Trump is] playing."
"Now he says it in a slightly different way: 'They would have to leave before they come back.' Well, how do they leave? ... He won the Republican nomination, in large measure, because he appealed to people who were quite attracted to that message -- the big wall that Mexico was going to pay for, which we now know is a sham, and deportation, which they're trying to somehow soften and move away from," she said.
"When someone shows you who he is, believe him," Clinton said.
"Trump has shown us repeatedly who he is, and what he would do if he were president, and that includes deporting 16 million people," the Democratic presidential nominee said.
Kaine said that in addition to the nation's 11 million undocumented immigrants, because Trump "wants to take away citizenship of children who were born here to parents without documents, that number swells to 16 million."
"The centerpiece of his campaign [has been] from that very first day when he so shockingly accused Mexican immigrants of being rapists and criminals [to] when he questioned the credibility of a federal judge, born in Indiana, of Mexican heritage," Clinton said. "Those kinds of comments and attacks that he has made consistently have placed him where he is today."