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Bar staffers are lucky they weren't seriously hurt in a brawl involving Cowboys stud Tyrone Crawford back in March ... TMZ Sports has obtained new video of the Florida fight, and TC was throwing BOMBS!!!

Crawford -- a Dallas team captain -- was the centerpiece of a melee inside of a Coyote Ugly bar on March 15 in Panama City Beach, FL.

In new footage we obtained of the whole brawl ... you can see how it all starts, with bouncers aggressively pulling a man by the neck through the crowd.

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A short time later, you can see Crawford -- a 6-foot-4, 285-pound D-lineman -- start getting violent with the bar staffers ... throwing some MASSIVE punches as well as a kick that nearly connects with a guy's head.

The brawl shifts from the heart of the venue to the exit ... where you can see Crawford throw EVEN MORE huge punches at Coyote Ugly staffers.

Eventually, the fight spills out of the bar's entrance ... but the punches don't stop -- Crawford swings several more times at bouncers -- connecting with a few of his looping punches.

The craziest part of the whole melee??? Video shows cops were in the middle of it all -- and still struggled to restrain the 29-year-old defensive lineman!!!

In fact, as cops are slapping the cuffs on one of Crawford's friends ... the Cowboys stud puts his hands on them to try to push them off!!!

Finally, cops and bouncers are able to control the situation ... with Crawford eventually getting separated from the fracas.

Tyrone was hit with a misdemeanor charge of affray for the altercation ... but he reached a deal with prosecutors in July to close out the criminal case ahead of Dallas' season.

We're told in exchange for completing an anger management assessment and keeping his nose clean for the next six months ... he'll have the charge dropped.

As for possible NFL punishment, Crawford said last month he had yet to speak with the league's investigators ... and added, "I did what I had to do as best I could."

"I am going to let God take it. I can’t speak on it too much. I am going to let God take it and handle everything, however it works out, it works out. Hopefully, they see my side."