What does Napoleon do to Jessie and Bluebell's puppies in Animal Farm?

The puppies were secretly trained to be guard dogs.

Like the milk and apples, the puppies also secretly disappear on the farm. They are part of Napoleon's plan to acquire and keep power for himself. He can’t adequately do that without a way to enforce his will. Since he is not bigger and stronger than the other animals, he needs someone who is, and who has teeth.

Napoleon is pretty quiet about what is actually...

The puppies were secretly trained to be guard dogs.

Like the milk and apples, the puppies also secretly disappear on the farm. They are part of Napoleon's plan to acquire and keep power for himself. He can’t adequately do that without a way to enforce his will. Since he is not bigger and stronger than the other animals, he needs someone who is, and who has teeth.

Napoleon is pretty quiet about what is actually happening with the puppies. They are mostly there one day and gone the next. He doesn’t tell anyone he is training them to be guard dogs, instead claiming he is educating them.

It happened that Jessie and Bluebell had both whelped soon after the hay harvest, giving birth between them to nine sturdy puppies. As soon as they were weaned, Napoleon took them away from their mothers, saying that he would make himself responsible for their education (Chapter 3).

It is around this time that the milk and apples also disappear, although the pigs claim it has nothing to do with privilege. The pigs say they deserve to have more because they are the leaders of the farm. They claim to need the milk and apples to keep the farm going and their brains working. 

When Snowball and Napoleon disagree at a meeting, the puppies reappear as ferocious guard dogs. They expel Snowball. From then on, anyone who disagrees with Napoleon is at risk because the dogs will threaten that animal. 

But suddenly the dogs sitting round Napoleon let out deep, menacing growls, and the pigs fell silent and sat down again. Then the sheep broke out into a tremendous bleating of "Four legs good, two legs bad!" which went on for nearly a quarter of an hour and put an end to any chance of discussion (Chapter 5).

Between the dogs threatening dissenters and the sheep drowning out the dissenters' voices, no one can disagree with Napoleon. After a while, no one will try. The dogs will kill anyone who confesses to be a traitor or is accused of being one.