The mass stranding was reported to the department on Sunday.
"Only 26 of the whales were still alive at this point, the majority of them appearing very weak, and were euthanised due to the rough sea conditions and almost certainty of there being great white sharks in the water which are brought in by a stranding like this", DOC Biodiversity Ranger Jemma Welch said, as quoted in a press release.
Another two whales stranded by Monday morning and also had to be euthanized, according to the authorities.
Mass strandings are common on the remote archipelago. The record stranding was registered in 1918 when up to 1,000 marine animals died as a result.