The COVID-19 pandemic has spawned a diverse body of scientific literature that is challenging to navigate, stimulating interest in automated tools to help find useful knowledge. We pursue the construction of a knowledge base (KB) of mechanisms---a fundamental concept across the sciences, which encompasses activities, functions and causal relations, ranging from cellular processes to economic impacts. We extract this information from the natural language of scientific papers by developing a broad, unified schema that strikes a balance between relevance and breadth. We annotate a dataset of mechanisms with our schema and train a model to extract mechanism relations from papers. Our experiments demonstrate the utility of our KB in supporting interdisciplinary scientific search over COVID-19 literature, outperforming the prominent PubMed search in a study with clinical experts. Our search engine, dataset and code are publicly available.