Here are the administration officials who have said that family separation is meant as a deterrent
...White House Chief of Staff John F. Kelly told NPR later that month that the policy had a specific intent.
"Are you in favor of this new move announced by the attorney general early this week, that if you cross the border illegally even if you're a mother with your children, to arrest you?" NPR's John Burnett asked. "We're going to prosecute you, we're going to send your kids to a juvenile shelter?"
"They're coming here for a reason," Kelly said of migrants fleeing violence in Central America. "And I sympathize with the reason. But the laws are the laws. But a big name of the game is deterrence."
Family separation would be a tough deterrent, Burnett noted.
"It could be a tough deterrent -- would be a tough deterrent," Kelly replied....
Even in March 2017, the idea was not new. Two weeks after Trump was inaugurated, a DHS official named John Lafferty raised the idea of using family separation as a deterrent in a town hall meeting for Citizenship and Immigration Services officials, according to documents obtained by NBC News.
Once Kelly left DHS to join the White House in July, the hunt for deterrent policies continued. During an August meeting, the New Yorker reported, a DHS official named Gene Hamilton told DHS officials "that over the next few days we'd need to generate paperwork laying out everything we could do to deter immigrants from coming to the U.S. illegally," one person said. Family separations reportedly were included in the mix.
Even over the past 24 hours, multiple administration officials have pointed to a possible deterrent effect in defense of the policy....
So it does appear that Pres Trump's cruelty is a calculated effort to be a deterrent.