The investigation of similarities and differences in the mechanisms of verbal and visuospatial creative thinking has long been a controversial topic. Prior studies found that visuospatial creativity was primarily supported by the right hemisphere, whereas verbal creativity relied on the interaction between both hemispheres. However, creative thinking also involves abundant dynamic features that may have been ignored in the previous static view. Recently, a new method has been developed that measures hemispheric laterality from a dynamic perspective, providing new insight into the exploration of creative thinking. In the present study, dynamic lateralisation index was calculated with resting-state fMRI data. We combined the dynamic lateralisation index with sparse canonical correlation analysis to examine similarities and differences in the mechanisms of verbal and visuospatial creativity. Our results showed that the laterality reversal of the default mode network, fronto-parietal network, cingulo-opercular network and visual network contributed significantly to both verbal and visuospatial creativity and consequently could be considered the common neural mechanisms shared by these creative modes. In addition, we found that verbal creativity relied more on the language network, while visuospatial creativity relied more on the somatomotor network, which can be considered a difference in their mechanism. Collectively, these findings indicated that verbal and visuospatial creativity may have similar mechanisms to support the basic creative thinking process and different mechanisms to adapt to the specific task conditions. These findings may have significant implications for our understanding of the neural mechanisms of different types of creative thinking.