Aside from the entire story being euphemistic for Communism, the events of the story are fairly clear and plain; Orwell does not shy away from showing the brutality of the pigs once they take power, and clearly states how some of the animals are killed. One good example of a euphemism comes when the pigs cut the rations of the other animals:
Once again all rations were reduced, except those of the pigs and the dogs... For the time being, certainly, it had been found necessary to make a readjustment of rations (Squealer always spoke of it as a 'readjustment,'never as a 'reduction')...
(Orwell, Animal Farm, msxnet.org)
This allows the act to be taken not as a deliberate limiting of the food supply, but simply part of the overall plan to make the farm more prosperous. Squealer is a master of double-talk, and so by avoiding the more negative term "reduction," he is able to reassure the animals that they are actually better off instead of starving and cold.
There are many euphemisms in Animal Farm. Arguably the most emotional one is when Boxer grows ill after working so diligently without questioning anything. When he literally works himself to sickness, the pigs do not take care of him, but send him away to be slaughtered and made into glue. Napoleon repays him with slaughter is the best way to put it.
When this happens, Squealer tries to explain things away. Yes, Boxer died but he died well in a hospital. Moreover, Boxer's last words were to press on with the rebellion. Euphemistic language, to be sure.
Three days later it was announced that he had died in the hospital at Will- ingdon, in spite of receiving every attention a horse could have. Squealer came to announce the news to the others. He had, he said, been present during Boxer’s last hours.
‘It was the most affecting sight I have ever seen!’ said Squealer, lifting his trotter and wiping away a tear. ‘I was at his bedside at the very last. And at the end, almost too weak to speak, he whispered in my ear that his sole sorrow was to have passed on before the windmill was finished. ’Forward, comrades!’ he whispered. ’Forward in the name of the Rebellion. Long live Animal Farm! Long live Comrade Napoleon! Napoleon is always right.’ Those were his very last words, comrades.’