The cat serves as comic relief and another example of Tom’s exploits when he feeds it painkillers.
Tom is feeling depressed because Becky hasn’t been to school in a while. He finds out that she is sick, and is afraid that she is going to die. His aunt loves to try out home remedies, so she sees this as an opportunity to test a new one. Tom asks for Pain-killer, and gives it to the cat.
Tom pretends to ask the cat if it wants medicine, with the cat saying it does. Of course, the cat does not really want medicine. Tom pries his mouth open and forces the Pain-killer on the cat, telling him that if he doesn’t like it he has no one to blame but himself. The poor cat certainly reacts.
Peter sprang a couple of yards in the air, and then delivered a war-whoop and set off round and round the room, banging against furniture, upsetting flower-pots, and making general havoc. (Ch. 12)
As the cat is doing “double somersaults,” Aunt Polly comes into the room. She of course asks Tom what “ails the cat” and he of course tells her he has no idea. He tells her the cat is just having a good time. Finally she sees the spoon, and he admits that he gave the cat the painkiller because he felt sorry for the cat for not having an aunt to give it to him.
Because if he’d had one she’d a burnt him out herself! She’d a roasted his bowels out of him ‘thout any more feeling than if he was a human!’ (Ch. 12)
This makes his aunt feel bad. She realizes that if the cat reacted that strongly to the medicine, it must be awful stuff. She fears that she has been treating Tom just as cruelly as he was to the cat by forcing it on him.
The incident serves as an example of comic relief, both because of Aunt Polly’s silly medicines and Tom’s messing with the cat. It makes the reader laugh, and also demonstrates Tom’s cleverness. Tom proved his point to his aunt, that the medicine was harmful to him. He gets out of having to take any more medicine.