Mark Twain's use of exaggeration is great in this story, and it is one of the aspects that makes it so humorous. For instance, in paragraph 5, Twain is describing the bull pup, Andrew Jackson, a fighting dog who has one strategy in every fight—to grab hold of his opponents' hind legs and hold until the other dog gives up. Twain uses exaggeration when describing the dog; for instance, the text says, "But as soon as money was up on him, he was a different dog—his underjaw'd begin to stick out like the fo'castle of a steamboat, and his teeth would uncover, and shine savage like the furnaces." Here, the dog is being given human characteristics, understanding that when money was being placed on him for a bet, he knew when to change strategies. Also, the description of his jaw, how it sticks out "like the fo'castle of a steamboat," not only showcases Twain's love of the Mississippi River and steamboats, but it's an exaggeration of how the dog looks menacing.
In paragraph 6, Twain moves to describe other animals that Jim Smiley used in betting, but most notably is the jumping frog for which this story is titled. Twain describes when Smiley found his frog: "He ketched a frog one day, and took him home, and said he cal'klated to edercate him; and so he never done nothing for three months but set in his back yard and learn that frog to jump." First, a frog would already know how to jump, so there is exaggeration in the idea of teaching a frog, or "educating" him as the story claims. In addition, the description of the frog jumping is so exaggerated that it makes the reader smile to imagine it: "you'd see that frog whirling in the air like a doughnut—see him turn one summerset, or may be a couple, if he got a good start, and come down flat-footed and all right, like a cat." All in all, Twain's descriptions and exaggerations make this an humorous story.