The outbreak of the novel Coronavirus Disease (COVID-19) has greatly influenced people's daily lives across the globe. Emergent measures and policies (e.g., lockdown, social distancing) have been taken by governments to combat this highly infectious disease. However, people's mental health is also at risk due to the long-time strict social isolation rules. Hence, monitoring people's mental health across various events and topics will be extremely necessary for policy makers to make the appropriate decisions. On the other hand, social media have been widely used as an outlet for people to publish and share their personal opinions and feelings. The large scale social media posts (e.g., tweets) provide an ideal data source to infer the mental health for people during this pandemic period. In this work, we propose a novel framework to analyze the topic and sentiment dynamics due to COVID-19 from the massive social media posts. Based on a collection of 13 million tweets related to COVID-19 over two weeks, we found that the positive sentiment shows higher ratio than the negative sentiment during the study period. When zooming into the topic-level analysis, we find that different aspects of COVID-19 have been constantly discussed and show comparable sentiment polarities. Some topics like ``stay safe home" are dominated with positive sentiment. The others such as ``people death" are consistently showing negative sentiment. Overall, the proposed framework shows insightful findings based on the analysis of the topic-level sentiment dynamics.