Napoleon's purpose is to demonize Snowball as much as he possibly can. He can use Snowball as the scapegoat for everything that goes wrong on the farm. In so doing, he can present himself as a foil to Snowball's evil. The gullible and unintelligent animals would, therefore, be convinced that he is truly their protector, acting in their best interests.
Before Snowball's expulsion, he and Napoleon were constantly at loggerheads about the management of the farm. They would constantly argue during meetings since they were in direct opposition to one another. Snowball would almost always gain support for his ideas since he was a quick thinker and quite innovative, whilst Napoleon surreptitiously went around influencing other animals, such as the sheep, to do his bidding. He would then use them during meetings to disrupt Snowball's eloquent speeches by constantly bleating, 'Four legs good, two legs bad.' Napoleon employed this pernicious tactic since he was not Snowball's equal when it came to acting in the best interests of the farm. He had other ideas and wanted to have sole control. Snowball was a thorn in his side and he had to get rid of him. He could do this once he had secretly raised Jessie and Bluebell's nine puppies and trained them to do his bidding. They had grown into ferocious dogs and he used them to chase Snowball off the farm.
Once Snowball was not there to challenge him any longer, Napoleon could freely go about and assert his authority. He started spreading lies and propaganda about Snowball, using Squealer especially. It was, for example, put out that Snowball had been a traitor from the very start and that he was actually fighting on the side of Mr. Jones during the Rebellion.
... it was given out that fresh documents had been discovered which revealed further details about Snowball’s complicity with Jones. It now appeared that Snowball had not, as the animals had previously imagined, merely attempted to lose the Battle of the Cowshed by means of a stratagem, but had been openly fighting on Jones’s side. In fact, it was he who had actually been the leader of the human forces, and had charged into battle with the words ‘Long live Humanity!’ on his lips. The wounds on Snowball’s back, which a few of the animals still remembered to have seen, had been inflicted by Napoleon’s teeth.
By sullying Snowball's name, Napoleon also destroyed whatever chance Snowball might ever have of returning to the farm. He also destroyed the hopes other animals might have of ever seeing their comrade again. This systematic propaganda campaign put him in good stead with the other animals. Boxer, for example, who expressed some doubt about the damaging claims made about Snowball, was easily persuaded since he believed that, 'Napoleon is always right.'
Using Snowball also gave Napoleon the perfect opportunity to rid himself of whatever animals were left to either expose him or threaten his authority. He conducted a purge in which many animals were slaughtered after confessing to having assisted Snowball during his seemingly secret visitations to the farm, apparently to do mischief and destroy the animals' hard work. Snowball was, for example, also blamed for mixing weed seeds in those of some crops that had been planted.
Napoleon's campaign worked well and the animals soon forgot about the positive role that Snowball had played on the farm. They truly believed that he was out to destroy their hard work. Whenever Napoleon wanted to manipulate the animals, he would use Snowball's name to back up his sentiments. He, for example, claimed that Snowball had been hiding on Frederick's farm when he was friends with Pilkington, and vice versa when he sought Frederick's support.
It now appeared that Snowball was not, after all, hiding on Pinchfield Farm, and in fact had never been there in his life: he was living — in considerable luxury, so it was said — at Foxwood, and had in reality been a pensioner of Pilkington for years past.
The animals were easily swayed by this topsy-turvy state of affairs and were more confused than ever by Napoleon's so-called 'clever tactics.' In the end, though, all memory of Snowball, and the memory of much of everything else, faded away.