Online hate speech detection has become an important issue due to the growth of online content, but resources in languages other than English are extremely limited. We introduce K-MHaS, a new multi-label dataset for hate speech detection that effectively handles Korean language patterns. The dataset consists of 109k utterances from news comments and provides a multi-label classification using 1 to 4 labels, and handles subjectivity and intersectionality. We evaluate strong baselines on K-MHaS. KR-BERT with a sub-character tokenizer outperforms others, recognizing decomposed characters in each hate speech class.