Social media has become an essential channel for posting disaster-related information, which provide governments and relief agencies real-time data for better disaster management. However, research in this field has not received sufficient attention and extracting useful information is still challenging. This paper aims to improve disaster relief efficiency via mining and analyzing social media data like public attitudes towards disaster response and public demands for targeted relief supplies during different types of disasters. We focus on different natural disasters based on properties such as types, durations, and damages, which contains a total of 41,993 tweets. In this paper, public perception is assessed qualitatively by manually classified tweets, which contain information like the demand for targeted relief supplies, satisfactions of disaster response, and public fear. Public attitudes to natural disasters are studied via a quantitative analysis using eight machine learning models. To better provide decision-makers with the appropriate model, the comparison of machine learning models based on computational time and prediction accuracy is conducted. The change of public opinion during different natural disasters and the evolution of people's behavior of using social media for disaster relief in the face of the identical type of natural disasters as Twitter continues to evolve are studied. The results in this paper demonstrate the feasibility and validation of the proposed research approach and provide relief agencies with insights into better disaster management.