The animal was found trapped in the straps, which were caught around its head, mouth, neck, body and legs, making it impossible for it to escape.
He was found by a gamekeeper on a hillside on the west coast of the island, where it was believed to have been grazing on seaweed when his antlers got stuck in the plastic waste.
The 32-year-old gamekeeper Scott Muir, who is one of just 230 people living on the island, believes the animal may have tried to walk up the hill for about a mile before falling down.
He said: “I was walking over the estate when I saw the plastic waste and realised there was a stag caught [in the plastic].
“I thought it was dead at first but as I approached it I could see his head start to move.
“These can be 18st animals and I know how powerful they can be, but he looked tired and stressed and he couldn’t see because the plastic was right around his antlers.
“He wouldn’t have been able to graze either as it was right over his mouth, so he was effectively starving.
“I think he has been there for about a week.
"In the end the animal had to be dispatched.”
Increasing plastic pollution
Mr Muir, who volunteers with Wild Side of Jura, a group aiming to protect the west coast and raise awareness to stop plans for a potential fish farm being built, said plastic pollution on the island has increased in the last five years.
He said: “We are a group of five or six volunteers who came together to protect the west coast of Jura and raise awareness of a fish farm which is trying to be built here.
“The plastic on the stag is not fishing net but plastic banding which is used in conjunction with fishing.
“We can’t categorically say where it came from but I'd be willing to bet some sort of commercial fishing, fish farm, which is what we are trying to stop on the west coast of Jura.”