Autism spectrum disorder (ASD) is one of the major developmental disorders affecting children. Recently, it has been hypothesized that ASD is associated with atypical brain connectivities. A substantial body of researches use Pearsons correlation coefficients, mutual information, or partial correlation to investigate the differences in brain connectivities between ASD and typical controls from functional Magnetic Resonance Imaging (fMRI). However, correlation or partial correlation does not directly reveal causal influences - the information flow - between brain regions. Comparing to correlation, causality pinpoints the key connectivity characteristics and removes redundant features for diagnosis. In this paper, we propose a two-step method for large-scale and cyclic causal discovery from fMRI. It can identify brain causal structures without doing interventional experiments. The learned causal structure, as well as the causal influence strength, provides us the path and effectiveness of information flow. With the recovered causal influence strength as candidate features, we then perform ASD diagnosis by further doing feature selection and classification. We apply our methods to three datasets from Autism Brain Imaging Data Exchange (ABIDE). From experimental results, it shows that with causal connectivities, the diagnostic accuracy largely improves. A closer examination shows that information flows starting from the superior front gyrus to default mode network and posterior areas are largely reduced. Moreover, all enhanced information flows are from posterior to anterior or in local areas. Overall, it shows that long-range influences have a larger proportion of reductions than local ones, while local influences have a larger proportion of increases than long-range ones. By examining the graph properties of brain causal structure, the group of ASD shows reduced small-worldness.