Weakly supervised semantic segmentation (WSSS) with image-level labels aims to achieve segmentation task without dense annotations. However, attributed to the frequent coupling of co-occurring objects and the limited supervision from image-level labels, the challenging co-occurrence problem is widely present and leads to false activation of objects. In this work, we devise a 'Separate and Conquer' training paradigm SeCo to tackle the co-occurrence challenge from dimensions of image space and feature space. In the image space, we propose to 'separate' the co-occurring objects with image decomposition by subdividing images into patches. Importantly, we assign each patch a category tag from Class Activation Maps (CAMs), which helps to identify objects at patch level and guide the subsequent representation. In the feature space, we propose to 'conquer' the false activation by enhancing semantic representation with multi-granularity knowledge contrast. To this end, a dual-teacher-single-student architecture is designed to extract knowledge at image level and patch level. Along with the knowledge and patch tags, class-specific contrast is conducted to facilitate the discrepancy among co-occurring objects. We streamline the multi-staged WSSS pipeline end-to-end and tackle co-occurrence without external supervision. Extensive experiments are conducted, validating the efficiency of our method tackling co-occurrence and the superiority over previous single-staged and even multi-staged competitors on PASCAL VOC and MS COCO. Codes will be publicly available soon.