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TMZ Sports has obtained police footage of NFL star Junior Galette being run down by cops -- and then tased -- following an alleged fight in Mississippi back in April ... and the footage is insane.

It all went down on April 8 ... when a Biloxi PD officer saw the Redskins linebacker fighting with another man and instructed them both to freeze. The cop claims Galette ignored instructions and bolted.

You can see the cop -- who identifies himself as a "big white guy" -- sprinting after Galette while shouting, "Stop motherf*cker! I'm gonna taze your ass!!"

Galette continues to run so the cop pulled out his taser and fired -- striking Junior on the first shot and putting the 250 pounder on the ground. The cop is obviously impressed with his own speed.

"I may be a big white guy, but you know what? I told you to stop."

Once he's down, Galette insisted he did nothing wrong ...but the cop disagrees.

Cop: "You’re swingin’ and hittin’ this guy right in front of me. I tell you to stop."

Junior: "He hit me sir."

Cop: "Y'all both hittin’ each other. I tell you to stop and then you take off running. If you’re gonna run from me when I tell you to stop after I see you hit him, I’m gonna chase after you and I’m gonna tase you."

Galette was eventually arrested for disorderly conduct and failure to comply. After he was put in the squad car and taken to the police station, the arresting officer can be heard doing some post-chase breakdown with his colleagues.

One of the cops keeps it real and says the officer who gave chase should chill 'cause Galette's a linebacker ... not exactly known for blazing breakaway speed.

Officials tell TMZ Sports ... Galette eventually struck a plea deal with prosecutors, though the details are unclear. However, we're told the case is effectively closed.