Sarcasm is a complex form of sentiment expression widely used in human daily life. Previous work primarily defines sarcasm as a form of verbal irony, which covers only a subset of real-world sarcastic expressions. However, sarcasm serves multifaceted functions and manifests itself through various rhetorical devices, such as echoic mention, rhetorical question and hyperbole. To fully capture its complexity, this paper investigates fine-grained sarcasm classification through the lens of rhetorical devices, and introduces RedSD, a RhEtorical Device-Aware Sarcasm Dataset with counterfactually augmented data.To construct the dataset, we extract sarcastic dialogues from situation comedies (i.e., sitcoms), and summarize nine rhetorical devices commonly employed in sarcasm. We then propose a rhetorical device-aware counterfactual data generation pipeline facilitated by both Large Language Models (LLMs) and human revision. Additionally, we propose duplex counterfactual augmentation that generates counterfactuals for both sarcastic and non-sarcastic dialogues, to further enhance the scale and diversity of the dataset.Experimental results on the dataset demonstrate that fine-tuned models exhibit a more balanced performance compared to zero-shot models, including GPT-3.5 and LLaMA 3.1, underscoring the importance of integrating various rhetorical devices in sarcasm detection. Our dataset is avaliable at https://github.com/qqHong73/RedSD.