Graham walked away from the wreck in the Miami area unscathed ... but when he broke it all down for media members at his press conference Tuesday, it's truly hard to fathom how he wasn't seriously injured in the crash.

The 34-year-old says it all initially happened because he saw a cop car going down an off-ramp with its reverse lights on.

"He was reversing," the Chicago Bears tight end said. "So I got over two lanes and, you know, the sun is kind of coming up, and as I go up over that hill, I'm looking at the cop and when I look up, there's a disabled vehicle on the center lane."

"And I'm going about 90. So, probably about 15 yards away, so I swerved to the left and barely missed him, but I was headed for a bridge so I had to make kind of a last-minute decision and decided to turn right and flip it to avoid jumping that thing."

Graham says cops told him he rolled his vehicle over FOUR times and skidded on his roof for about 100 yards.

Somehow, though, Jimmy says he and his dog were able to simply get out of the ride after it came to a stop and walk away.

"Sparks and glass is going everywhere and I'm just sitting there in the seat belt," Jimmy said. "I get out the seat belt and I'm on the roof kind of hollering for my dog. I don't hear her so I get out and she's in the back and we just walked way."

"Couple hours later, ended up flying [out for a charity event]. So, it was a wild one."