Graph Neural Networks (GNNs) have been widely used in various domains, and GNNs with sophisticated computational graph lead to higher latency and larger memory consumption. Optimizing the GNN computational graph suffers from: (1) Redundant neural operator computation. The same data are propagated through the graph structure to perform the same neural operation multiple times in GNNs, leading to redundant computation which accounts for 92.4% of total operators. (2) Inconsistent thread mapping. Efficient thread mapping schemes for vertex-centric and edge-centric operators are different. This inconsistency prohibits operator fusion to reduce memory IO. (3) Excessive intermediate data. For GNN training which is usually performed concurrently with inference, intermediate data must be stored for the backward pass, consuming 91.9% of the total memory requirement.To tackle these challenges, we propose following designs to optimize the GNN computational graph from a novel coordinated computation, IO, and memory perspective: (1) Propagation-postponed operator reorganization. We reorganize operators to perform neural operations before the propagation, thus the redundant computation is eliminated. (2) Unified thread mapping for fusion. We propose a unified thread mapping scheme for both vertex- and edge-centric operators to enable fusion and reduce IO. (3) Intermediate data recomputation. Intermediate data are recomputed during the backward pass to reduce the total memory consumption. Extensive experimental results on three typical GNN models show that, we achieve up to 2.75x end-to-end speedup, 6.89x less memory IO, and 7.73x less memory consumption over state-of-the-art frameworks.