Napoleon had his reasons for taking away Jessie and Bluebell's puppies: he wanted them for his own nefarious purposes. According to Chapter 3, there were nine puppies in all. As soon as the puppies were weaned, Napoleon took them away from their mothers.
Napoleon's actions encapsulate Orwell's beliefs about totalitarian leaders (whether capitalist or socialist), especially their tendency to indoctrinate the young for exploitative purposes.
In chapter 5, we discover that Napoleon has trained the nine puppies to serve as members of his attack squad. The text tells us that the puppies are not yet full-grown. However, they are rugged dogs, and their large size intimidates the other animals. Upon Napoleon's order, a "high-pitched whimper of a kind no one had ever heard him utter before," the nine dogs lunge for Snowball.
Napoleon's attack squad summarily drives Snowball out of the farm. After this terrifying incident, Napoleon immediately takes center stage and acts as the de facto leader of Animal Farm. He announces that there will be no more debates and that he will be giving the orders from now on.
So, Napoleon took away Jessie and Bluebell's puppies to exploit for his own gain. However, he publicly maintained that "the education of the young was more important than anything that could be done for those who were already grown up." For their part, the animals did not realize Napoleon's true meaning: adults are far harder to manipulate and indoctrinate than the young. Thus, Napoleon had to claim the young for his own before they adopted values that were antithetical to his goals.