Amelia Dean was attacked while walking through a state park in South Dakota on the second day of her gap year trip. She was due to start at the University of Edinburgh in September.
Ms Dean was walking with a friend and his dog on a trail in Custer State Park when they spotted the bison around 100 yards away.
The 2,000-pound bison soon charged at Miss Dean, gorged her left thigh with its horn and threw her 10-15 feet in the air.
Her family said she is lucky to be alive “as she should have bled out in two-eight minutes after the severed artery and the ambulance didn’t arrive for 20 minutes”.
They added: “It is a miracle that she is alive today.”
Miss Dean sustained a completely severed femoral artery and severe damage to both her tibial and peroneal nerves (part of the sciatic nerve) from the attack.
While the artery and muscle damage is understood to be healing, she is still suffering from severe nerve pain, paralysis, limited mobility below the knee and more.
The young girl said: “I have basically no movement in my foot. I can’t walk without a walker or crutches.
“I can’t walk very far, about [22 yards], and I’m done for a long time.”
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They are now raising funds to get Miss Dean moved elsewhere for full treatment.
Mr and Mrs Dean wrote on a GoFundMe page: “No treating doctors feel comfortable indicating that Mia is safe to fly, and the peripheral nerve specialist from Mayo Clinic states that he cannot make any real assessments until he has personally seen her.
“Mia is English and while her travel insurance has paid so far for the femoral artery bypass they are refusing to pay for even the initial examination by the specialist of her nerve injury.
“Mayo Clinic, a world-class hospital in the peripheral nerve field (a very niche field), has accepted Mia as a referral from Rapid City Hospital.”
They added that “this could be Mia’s best chance to regain control of her foot, and time is running out”.
As of 8am this morning, more than £17,000 of a £140,000 total target had been raised.