This paper describes SciClops, a method to help combat online scientific misinformation. Although automated fact-checking methods have gained significant attention recently, they require pre-existing ground-truth evidence, which, in the scientific context, is sparse and scattered across a constantly-evolving scientific literature. Existing methods do not exploit this literature, which can effectively contextualize and combat science-related fallacies. Furthermore, these methods rarely require human intervention, which is essential for the convoluted and critical domain of scientific misinformation. SciClops involves three main steps to process scientific claims found in online news articles and social media postings: extraction, clustering, and contextualization. First, the extraction of scientific claims takes place using a domain-specific, fine-tuned transformer model. Second, similar claims extracted from heterogeneous sources are clustered together with related scientific literature using a method that exploits their content and the connections among them. Third, check-worthy claims, broadcasted by popular yet unreliable sources, are highlighted together with an enhanced fact-checking context that includes related verified claims, news articles, and scientific papers. Extensive experiments show that SciClops tackles sufficiently these three steps, and effectively assists non-expert fact-checkers in the verification of complex scientific claims, outperforming commercial fact-checking systems.