Dynamic graph neural networks (DGNNs) are increasingly vital for modeling evolving graph-structured data across diverse applications. However, existing methods often incur significant computational redundancy by processing large portions of the graph—even when updates are localized and sparse. In this paper, we present ATLAS, a high-performance DGNN framework that enables abstraction-driven incremental execution through tight algorithm-system co-design. At the algorithmic level, ATLAS constructs lightweight, connectivity-aware graph abstractions anchored at influential nodes, enabling fine-grained and efficient propagation of dynamic updates. At the system level, it applies abstraction-driven scheduling and memory optimizations to balance workload and enhance locality, achieving efficient parallel execution. Extensive experiments demonstrate that ATLAS outperforms current state-of-the-art systems, achieving speedups of 2.44 \(\times \) , 3.17 \(\times \) , 5.91 \(\times \) , and 10.57 \(\times \) over RACE, DeltaGNN, DGL, and PyG, respectively, while incurring only negligible accuracy loss (less than 1%).