Sarcasm poses a challenge in linguistic analysis due to its implicit nature, involving an intended meaning that contradicts the literal expression. The advent of social networks has propelled the utilization of multimodal data to enhance sarcasm detection performance. In prior multimodal sarcasm detection datasets, a single label is assigned to a multimodal instance. Subsequent experiments often highlight the superiority of multimodal models by demonstrating their improvements compared to unimodal models based on these unified labels across multiple modalities. However, our investigation revealed that numerous instances of sarcasm cannot be identified using a single modality. Humans employ the conflict between a statement and factual information as a cue to detect sarcasm, and these cues can stem from different modalities. Then, a unified label for a multimodal instance may be not suitable for the associated text or image. In this work, we introduce SarcNet, a multilingual and multimodal sarcasm detection dataset in English and Chinese, consisting of 3,335 image-text pair samples. We provide annotations for sarcasm in visual, textual, and multimodal data, respectively, resulting in over 10,000 labeled instances. The separated annotation schema for unimodal and multimodal data facilitates a more accurate and reasonable assessment of unimodal and multimodal models.