Dickens compares both Pip and Provis to dogs several times in Great Expectations. This simile is used to explain a difference in power between characters, and also to indicate animalistic or uncivilized actions in the "dog"-like figure. In. Chapter 3, when Pip brings Provis food and drink as he hides in the marshes, he compares the convict directly to an animal he knows:

I had often watched a large dog of ours eating his food; and I now noticed a decided similarity between the dog’s way of eating, and the man’s. The man took strong sharp sudden bites, just like the dog. He swallowed, or rather snapped up, every mouthful, too soon and too fast; and he looked sideways here and there while he ate, as if he thought there was danger in every direction [...] he was very like the dog.

Provis has reverted to an animal-like state after his escape from the prison-barge, as he snaps and bites at his provisions. Pip is frightened, but he also feels sympathy for Provis as he would for a hungry dog. The sense of desperation Provis feels is amplified by the frantic language Dickens uses here; Provis doesn't eat, he "swallows" his food "too soon and too fast." 

When the simile of the dog occurs in Great Expectations it always indicates a difference in status. This is true between Pip and Provis above, but also between Pip and Estella when she treats him "like a dog in disgrace." She makes him follow her like a dog and treats him as subhuman until much later in the novel. When Provis first meets Pip he calls him a "young dog" and a "fierce young hound," foreshadowing their later connection. Finally, when Provis reveals that it is himself and not Miss Havisham who is Pip's patron, he refers again to this simile, calling himself an "old dunghill dog." The human-and-dog relationship in literature is a classic trope of superior and subordinate, and Dickens uses it as shorthand here to indicate unequal relationships and social standings.