Donald Trump was in great spirits Tuesday morning ... and why wouldn't he be, 'cause he was talking about one of his favorite ...

Video taken by Kelly Alvarez shows the adult alligator chomping down on a baby alligator in Shark Valley Everglades National Park on Sunday, May 11, as two young gators watch nearby.

"The victim was immediately bitten on the torso, and efforts by her husband to assist her were unsuccessful," FWC's report ...