Online abusive language detection (ALD) has become a societal issue of increasing importance in recent years. Several previous works in online ALD focused on solving a single abusive language problem in a single domain, like Twitter, and have not been successfully transferable to the general ALD task or domain. In this paper, we introduce a new generic ALD framework, MACAS, which is capable of addressing several types of ALD tasks across different domains. Our generic framework covers multi-aspect abusive language embeddings that represent the target and content aspects of abusive language and applies a textual graph embedding that analyses the user’s linguistic behaviour. Then, we propose and use the cross-attention gate flow mechanism to embrace multiple aspects of abusive language. Quantitative and qualitative evaluation results show that our ALD algorithm rivals or exceeds the six state-of-the-art ALD algorithms across seven ALD datasets covering multiple aspects of abusive language and different online community domains.