Sarcasm is a form of irony used to mock or convey contempt, which occurs when there is an incongruity between the literal meaning of an utterance and its intended meaning. Many studies identify sarcasm by capturing the incongruity in-between the words. However, consider the following example, “I love waking up at 4 am on Saturday”, there is no apparent incongruity in-between the words. Intuitively, the word “love” and the snippet “waking up at 4 am on Saturday” form a strong contrast. Thus, capturing the incongruity among the sentence snippets is more reasonable since a sentence snippet usually contains more semantic information than a single word. Additionally, not all snippets are equally important when human beings identify sarcasm. Thus, inspired by the above observations, we propose the Self-Attention of Weighted Snippets (SAWS) model for sarcasm detection, which overcomes the problem that the previous models are inefficient in determining the sarcasm caused by snippet incongruity. The experiment results show that our model achieves state-of-the-art performance on four benchmark datasets, including two short text Twitter datasets and two long text Internet Argument Corpus (IAC) datasets.