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Social media has been a vital channel for communicating and broadcasting disaster-related information. However, the global spatiotemporal patterns of social media users’ activities, interactions, and connections after a natural disaster remain unclear. Hence, we integrated geocoding, geovisualization, and complex network methods to illustrate and analyze the online social network’s spatiotemporal evolution. Taking the super typhoon Haiyan as a case, we constructed a retweeting network and mapped this network according to the tweets’ location information. The results show that (1) the distribution of in-degree and out-degree follow power-law and retweeting networks are scale-free. (2) A local catastrophe could attract significant global interest but with strong geographical heterogeneity. The super typhoon Haiyan especially attracted attention from the United States, Europe, and Australia, in which users are more active in posting and forwarding disaster-related tweets than other regions (except the Philippines). (3) The users’ interactions and connections are also significantly different between countries and regions. Connections and interactions between the Philippines and the United States, Europe, and Australia were much closer than in other regions. Therefore, the agencies and platforms should also pay attention to other countries and regions outside the disaster area to provide more valuable information for the local people.