Deputies said the woman was transferring her ex-boyfriend's belongings and picked up the pet crate that contained the cat and threw it into the water.
The 17-year-old was trying to find his surfboard when the shark attacked him.
Beach safety officials said the shark bite was the third such incident recorded this year in Volusia County.
The pair are accused of theft during a declared state of emergency as the East Coast prepares for the powerful storm.
The president of the Volusia United Educators union acknowledged Brian Wheeler had made a poor decision performing the chore naked.
Florida is the U.S. state where most shark attacks occur—indeed, it has the highest incidence of attacks in the world.
Richard Lewis reportedly admitted to police he attempted to poison his ex-girlfriend by putting cleaning product in her juice because he was "frustrated" during their breakup.
Jesse Estep, 29, was arrested after he "intentionally swerved and drove the mail truck directly toward" deputies in Flagler County on June 8, the sheriff's office said.
Julie Edwards has been charged with driving under the influence of alcohol, making a threat against a law enforcement officer, refusing to submit for testing and resisting an officer without violence.
"He is a soulless individual who thought he was gonna outsmart everyone," said Volusia County Sheriff Mike Chitwood.
The four students might have to pay over $1,000 in fees because of the school threats.