Human activity recognition (HAR) requires extracting accurate spatial-temporal features with human movements. A mmWave radar point cloud-based HAR system suffers from sparsity and variable-size problems due to the physical features of the mmWave signal. Existing works usually borrow the preprocessing algorithms for the vision-based systems with dense point clouds, which may not be optimal for mmWave radar systems. In this work, we proposed a graph representation with a discrete dynamic graph neural network (DDGNN) to explore the spatial-temporal representation of human movement-related features. Specifically, we designed a star graph to describe the high-dimensional relative relationship between a manually added static center point and the dynamic mmWave radar points in the same and consecutive frames. We then adopted DDGNN to learn the features residing in the star graph with variable sizes. Experimental results demonstrated that our approach outperformed other baseline methods using real-world HAR datasets. Our system achieved an overall classification accuracy of 94.27\%, which gets the near-optimal performance with a vision-based skeleton data accuracy of 97.25\%. We also conducted an inference test on Raspberry Pi~4 to demonstrate its effectiveness on resource-constraint platforms. \sh{ We provided a comprehensive ablation study for variable DDGNN structures to validate our model design. Our system also outperformed three recent radar-specific methods without requiring resampling or frame aggregators.