Rudy Eugene, 31, was gunned down after the gruesome attack off the city's MacArthur Causeway, with the aftermath captured on film by a Miami Herald surveillance camera.
An old mug shot of Eugene was shown on the station as his former wife told the channel she had not spoken to him for more than three years.
The woman, named by the Miami Herald as Jenny Ductant, said: "I wouldn't say he had [a] mental problem but he always felt like people was against him...No one was for him, everyone was against him."
She claimed his increasing violence had led to their divorce in 2007, adding "That's why I left."
Court records show Eugene had been arrested eight times since the age of 16, once for a battery charge which was later dropped.
Eyewitness Larry Vega told WSVN-Fox 7 he saw a man biting the victim's face.
The cyclist notified police, who ordered the man to stop.
Vega added: "The guy just stood, his head up like that, with pieces of flesh in his mouth. And he growled."
The officer fired, but the man continued to chew, prompting him to continue shooting, eventually killing him.
The New York Daily News quoted Vega as saying: "The guy - he was like a zombie, blood dripping, it was intense. The closest thing I've seen to it? 'The Walking Dead'."
Police say Eugene may have been suffering from a drug-induced mania which causes the body to heat up, causing some users to strip off, the Miami Herald reported.
Armando Aguilar of the Miami Fraternal Order of Police suggested the drug may have been a new form of LSD.
The identity of Eugene's victim, also believed to be a homeless man, has not been released. He is in a critical condition at Jackson Memorial Hospital.
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