Trump ends the tirade, in which he calls Baron Cohen a "third rate character", by wishing the comedian be "punched in the face so many times he'd be in hospital", finally advising him to "go to school, learn about being funny".
The clip that Cohen revealed Sunday afternoon featured a clip of Dick Cheney signing what he was told was a "waterboarding kit".
"Sure!" Cheney said. "That's a first". Check out the teaser videos above and see the Trump promo clip below.
Sacha Baron Cohen arrives at the LA premiere of Alice Through The Looking Glass (AP) Sacha Baron Cohen/Borat poses for photographers during the Photocall for "Borat-The Movie" on the beach in Cannes.
"Sacha is a comedic genius who shocks you with his audacity, bravery and inventiveness", said Showtime president and CEO David Nevins. Behind the elaborate setup is a genuine quest for the truth about people, places and politics.
In a trailer, former US defense secretary Dick Cheney is pictured signing what is described as a water-boarding kit, and saying, "I hope you'll tune in next week for an interview with me".
The new Sacha Baron Cohen show will premiere on Showtime July 15.
Written and directed by Baron Cohen, the seven episodes series will begin on the Showtime cable channel in the States from this Sunday, before screening on Mondays in the UK.