The students saw people, thought to be DOC staff, trying to pull the whale out of the waves with a rope.
"Instead of pulling away from the whale, the digger was leaning towards the whale," Angus said.
The male whale was the average size of a physically mature adult and its blood turned the water and waves around it red, the pupils said.
A DOC ranger on-site explained to the kids that it could have been attacked by orcas or a squid, St Patrick's Catholic School teacher Kate Smith said.
Year 6 Lena Vo said: "We were sad, but our teacher said it had probably had a long life. Then we said the prayer 'our father' so that the whale would find peace."
Hawke's Bay DOC ranger Jamie Quirk said nothing could have saved the whale.
"It was just nature taking its course."
Poesy Hyde hung around with Lena after the whale had died and said they saw "three diggers rolling the whale further up the sand".
Local Mahia iwi, Ngāti Rongomaiwahine, collected the jawbone on Friday afternoon. The process of cutting through the jawbone took hours.
Over the weekend, following a traditional ceremony, the sperm whale was laid to rest by Mahia hapū members, a DOC spokesperson said.
The students on Monday told Hawke's Bay Today they were far from traumatised by the experience and considered themselves "lucky" to have seen it and been able to give it a farewell.