Polk County deputies responded to multiple calls about a man yelling for help at about 4 a.m. (0900 GMT). They could not shoot the animal because it was too dark, the sheriff's office said.
Adrian J. Apgar, 45, was taken to the hospital in critical condition with his left arm hanging by a tendon. He also had an apparent broken right arm and leg injuries.
"I remember him saying, 'I'm over here, get here quick, he's still got me, he's going to kill me, my arms are broken,"' deputy Michael Parker said.
It was not clear why Apgar was in the lake, reports AP.
Four deputies struggled to get the 250-pound (113-kilogram) man out of the water and thick brush, even after the alligator let Apgar loose. No deputy was injured.
The men said they were scared but did not have time to think.
"It was a human being, he was dying. He needed help," deputy Billy Osborne said.
The alligator believed to have bitten the man was caught several hours later after officials set out bait. Though there is no way to be certain the gator was the right one, the animal caught was aggressive and found near the attack site.
Russia may terminate all kinds of military and military-technical relations with Israel, including the agreement on the exchange of reconnaissance data
The Ilyushin 20 (Il-20) military electronic reconnaissance aircraft of the Russian Air Force with 14 servicemen on board that went off radar screens off the coast of Syria was shot down by Syrian air defense systems over the Mediterranean Sea