Witnesses said Mantella made an effort to leave the sidewalk and harass the animals by intentionally kicking them in the head.
Officials said they are monitoring the conditions of the swans.
"I guess he was, like, (practicing) karate kicks or something, and just, like, at one point, he just kicked it right in the head," witness David Camp said. "And I was like what was this guy doing?"
Police arrested Mantella after finding him walking around the lake.
Thursday's alleged incident wasn't the first incident involving the park's iconic swans.
In June 2016, an off-duty officer said she witnessed a man punch a swan in the head. Weeks earlier, half a dozen cygnets were taken from their mother. They were never found.
In 2013, a swan was euthanized after a dog attack. In 2012, a man was seen pulling a swan by its neck.
Mantella was charged with trespassing at Disney Springs three days ago. Records said he was arrested after he returned to the complex after trying to steal a cigarette from a couple in March. That charge was dropped.
Mantella remains jailed on $1,000 bail.