On Tuesday, Jones-Drew tweeted: "I guess death threats towards me and my family isn't head line news but me tweeting my opinion about a person is... The society is backwards I guess we haven't came far enough as human beings.
"When has a threat towards a person especially now. Has gone unspoken about on any national stage is outrages and unbelievable."
Earlier Tuesday, Jones-Drew apologized for his tweets about Cutler.
"It was my opinion, but I never wanted to personally attack Jay," Jones-Drew told The Florida Times-Union. "It's something that I hope it blows over. I was trying to have fun, have a joke, and I think it was something I should've never tweeted and I'm sorry for it. It was never to hurt him. Hopefully he can understand that, and everyone else can."
Jones-Drew said he was rooting for Cutler and the Bears in Sunday's NFC Championship Game, and when the quarterback left in the third quarter with an injury, the running back believed it was the perfect time to poke fun at the Florida Gators.
"Hey I think the urban meyer rule is effect right now... When the going gets tough........QUIT," Jones-Drew posted on his Twitter page.
Cutler was diagnosed Monday with sprained medial collateral ligament in his left knee.
"I never attacked him, called him soft or a sore loser," Jones-Drew told The Associated Press on Monday. "I never questioned his toughness. I think people took my joke out of context. I was taking at shot at Florida fans."
Jones-Drew acknowledged that Cutler's injury was serious enough for him to leave the game. But when Jones-Drew sent the tweet, he was unaware that anything was wrong with the quarterback.
"All I thought about was being in that position, being in that game," said Jones-Drew, who played on an injured knee for 14 games before missing the final two. "I've never been in a title game, so my first thought was, why wouldn't you want to play in that situation?"
The Associated Press contributed to this report.