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The worldwide spread of COVID-19 dramatically influences the world economic landscape. In this paper, we have quantitatively investigated the time-frequency co-movement impact of COVID-19 on U.S. and China stock market since early 2020 in terms of daily observation from National Association of Securities Dealers Automated Quotations Index (NDX), Dow Jones Industrial Average (DJIA), Standard & Poor's 500 Index (SPX), Shanghai Securities Composite Index (SSEC), Shenzhen Securities Component Index (SZI), in favor of spatiotemporal interactions over investor sentiment index, and propose to explore the divisibility and the predictability to the volatility of stock market during the development of COVID-19. We integrate evidence yielded from wavelet coherence and phase difference to suggest the responses of stock market indexes to the COVID-19 epidemic in a long-term band, which could be roughly divided into three distinguished phases, namely, 30–75, 110–150, and 220–280 business days for China, and 80–125 and 160–175 after 290 business days for the U.S. At the first phase, the reason for the extreme volatility of stock market mainly attributed to the sudden emergence of the COVID-19 epidemic due to the pessimistic expectations from investors; China and U.S. stock market shared strongly negative correlation with the growing number of COVID-19 cases. At the second phase, the revitalization of stock market shared strong simultaneous moves but exhibited opposite responses to the COVID-19 impact on China and U.S. stock market; the former retained a significant negative correlation, while the latter turned to positively correlated throughout the period. At the third phase, the progress in vaccine development and economic stimulus began to impose forces to stock market; the vulnerability to COVID-19 diminished to some extent as the investor sentiment indexes rebounded. Finally, we attempted to initially establish a coarse-grained representation to stock market indexes and investor sentiment indexes, which demonstrated the homogenous spacial distribution in the vectorgraph after normalization and quantization, implying the strong consistency when filtering the frequent small fluctuations during the evolution of the COVID-19 pandemic, which might help insights into the prediction of possible status transition in stock market performance under the public health issues, potentially performing as the quantitative references in reasonably deducing the economic influences.