Optimizing Deep Neural Networks (DNNs) to obtain high-quality models for efficient real-world deployment has posed multi-faceted challenges to machine learning engineers. Existing methods either search for neural architectures in heuristic design spaces or apply low-level adjustments to computation primitives to improve inference efficiency on hardware. We present Automated Graph Optimization (AutoGO), a framework to evolve neural networks in a low-level Computation Graph (CG) of primitive operations to improve both its performance and hardware friendliness. Through a tokenization scheme, AutoGO performs variable-sized segment mutations, making both primitive changes and larger-grained changes to CGs. We introduce our segmentation and mutation algorithms, efficient frequent segment mining technique, as well as a pretrained context-aware predictor to estimate the impact of segment replacements. Extensive experimental results show that AutoGO can automatically evolve several typical large convolutional networks to achieve significant task performance improvement and FLOPs reduction on a range of CV tasks, ranging from Classification, Semantic Segmentation, Human Pose Estimation, to Super Resolution, yet without introducing any newer primitive operations. We also demonstrate the lightweight deployment results of AutoGO-optimized super-resolution and denoising U-Nets on a cycle simulator for a Neural Processing Unit (NPU), achieving PSNR improvement and latency/power reduction simultaneously. Code available at https://github.com/Ascend-Research/AutoGO.