The slaughter, by rifle-fire from helicopters, is the work not of hunters but of the US Fish and Wildlife Service, which says it is saving the reindeer from a more painful death - starvation - this winter. Of a herd of about 900, about 580 have been killed so far. A lucky few have been airlifted away in privately sponsored mercy flights aboard an antique DC-3 cargo plane.
The cull was temporarily suspended three weeks ago, ostensibly because of the onset of the long Arctic nights and freezing conditions. But Wildlife Service officials admit they were unprepared for the strength of public protest, from local native communities and from animal lovers across the US.
No one disputes, however, that the plight of the reindeer, stranded on deserted Hagemeister Island two miles off Alaska's west coast, is genuine. They are the progeny of a herd of just 150 introduced to the island in 1965 by an Inuit entrepreneur, Jack Gosuk, who intended to farm them for meat and their antlers. But the herd was poorly managed and ballooned in size. Last spring Mr Gosuk gave it up, selling it to the Wildlife Service for one dollar.
The animals are now in crisis because the island, just 24 miles long, no longer has the vegetation to support them. Crucially, the lichen which reindeer find in winter by pawing away the snow has all but been exhausted.
'We have a responsibility to bring a swift and merciful end to animals that won't survive,' Jeff Stroebele of the Wildlife Service said from Anchorage this week. 'But I admit our timing was awful. We thought we were doing the humanitarian thing and suddenly - like Donner und Blitzen - Santa Claus comes crashing over the horizon.' Complaining that the exercise has cost his office more than dollars 100,000 (pounds 65,000), Mr Stroebele added with a tired sigh: 'Everybody thinks immediately about Rudolf and his red nose instead of an animal out there suffering.'
Nor is this the only wildlife controversy to involve Alaska. The state was forced on Tuesday to back down from plans to carry out a similar cull of grey wolves, endangered or extinct in most other US states, as a way to protect the populations of moose and caribou which attract hunters and therefore tourists' dollars.
The Wildlife Service went to lengths to soften local anger at the reindeer cull. It chartered a plane and flew back nearly 200 dressed carcasses and gave them to local villages on the mainland for meat. But that was abandoned when the aircraft went nose-down in the sand and broke its propeller.
Then, when the shooting was in full swing, a local doctor, Donald Olson, launched his own private airlift, hoping to get all the remaining animals off the island alive. He also made beach landings in his DC-3 Dakota and managed to corral 40 reindeer on board for three flights - saving 120 - before giving up.
Now the island has been submerged in the Arctic winter, and the Wildlife Service and the villages on the mainland coast are in a stand-off about what to do about the 200-odd animals left behind.