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The accident happened on State Highway 1, north of Dunedin, as Tommy-lee Winder (20) and partner Anna Whitmore (18) were heading home about 10.30pm on Wednesday.
Ms Whitmore was driving, when a large stag suddenly appeared "out of nowhere" on the side of the road near Hawksbury and then stepped into the path of their Toyota Corolla, Mr Winder said.
He happened to be glancing behind him at the time "when I heard my partner scream at the top of her lungs".
"I looked forward and saw the deer for a split second and my partner put the brakes on, but we hit it instantly.
"I had to grab the steering wheel to steer us to the side of the road as she was braking."
The couple’s vehicle was "completely written off" by the impact, while the stag suffered two broken legs but survived the initial crash.
The couple attempted to care for the animal, but it had to be euthanased by a vet soon after, he said.
Mr Winder and his partner escaped injury, although she was taken straight to Dunedin Hospital by ambulance for checks.
"It was an extremely scary thing to happen when your baby’s due in two or three weeks ... It could have simply gone through the windscreen and hit my partner but we were extremely lucky."