Floyd Mayweather and John Gotti III's exhibition match ended in complete chaos on Sunday night ... with multiple brawls breaking out after the two fighters got done with each other in the ring.

The scene at FLA Live Arena in Sunrise, Fla was absolute mayhem ... after Mayweather toyed with Gotti III for several rounds, the New York mob boss' grandson kicked off a melee by trying to go after the boxing legend.

You can see in video filmed by bystanders in the arena, after Gotti III was disqualified for holding in the sixth round, he attempted to still throw punches at Mayweather ... which led to several people jumping into the ring to protect the 50-0 boxer.

More than a dozen people got involved ... and while most of the scuffle featured pushing and shoving -- several punches were thrown.

Mayweather did not appear to be involved in any of the mayhem -- he was seen retreating to his corner away from all the action -- but the fracas lasted several minutes nonetheless.

Eventually, order was restored in the ring ... but that didn't stop some from misbehaving throughout the arena regardless.

As people were making their way back into the locker room area ... some were seen still going after each other -- with more punches being thrown.

Things didn't look much better in the bowels of the venue as well ... as "Love & Hip Hop" star Joseline Hernandez beat up Big Lex in a wild fight.

At some point, however, cooler heads finally prevailed ... and our sources say Mayweather actually took the time out to smooth things over with Gotti III.

We're told TBE and two others from his camp met with the boxer and chatted things over ... and there's now talks for the two to potentially rematch down the line.