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Mapping spacetime disease rates can provide a more in-depth understanding of their distribution and trends. Traditional spatiotemporal kriging methods can break the constraints of geopolitical boundaries and time intervals. Still, disease rates in densely and sparsely populated areas are stabilized to the same degree, resulting in a map that is oversmoothed in some places but undersmoothed in others. The stabilized spatiotemporal kriging method proposed in this study overcomes this problem by allowing for nonconstant variances over space and time. A spatiotemporal map of the standardized incidence ratio for oral cancer in men in Taiwan between 1997 and 2017 reveals that the high-risk areas for oral cancer are in the midwestern and southeastern regions of Taiwan, spreading toward the center and north, with persistent cold spots in the northern and southwestern urban regions. However, the corresponding map for breast cancer in women in Taiwan reveals that the high-risk areas for breast cancer are concentrated in densely populated urban regions in the west. Spatiotemporal maps facilitate our understanding of disease risk dynamics. We recommend using the proposed stabilized spatiotemporal kriging method for mapping disease rates across space and time.