Cleveland Browns star lineman Wyatt Teller hunted, shot and killed a 10-foot gator in Florida this week .... and then picked up the beast with his bare hands!!

Seriously!!

Here's how it went down -- Teller linked up with his buddy and Miami Dolphins defensive end Zach Sieler ... who happens to own a hunting outfitter, Clay Gully Outfitters, in central Florida.

The 2 NFL players -- who have been planning the trip for a while -- hunted hogs and gators on Sieler's enormous plot of land.

Sieler and his GF Hannah Cook tell TMZ Sports the 26-year-old All-Pro killed the gator -- which Zach estimates were 9.5 feet and 200 pounds -- and then threw it over his shoulder and carried it away.

FYI -- folks down south love to eat fried gator ... but no word on what will happen with this particular beast -- it could be eaten, or used to make a cool rug or even gator boots!!

Either way, it's gonna get used up.