Multi-exit network is a promising architecture for efficient model inference by sharing backbone networks and weights among multiple exits. However, the gradient conflict of the shared weights results in sub-optimal accuracy. This paper introduces Deep Feature Surgery (DFS), which consists of feature partitioning and feature referencing approaches to resolve gradient conflict issues during the training of multi-exit networks. The feature partitioning separates shared features along the depth axis among all exits to alleviate gradient conflict while simultaneously promoting joint optimization for each exit. Subsequently, feature referencing enhances multi-scale features for distinct exits across varying depths to improve the model accuracy. Furthermore, DFS reduces the training operations with the reduced complexity of backpropagation. Experimental results on Cifar100 and ImageNet datasets exhibit that DFS provides up to a 50.00% reduction in training time and attains up to a 6.94% enhancement in accuracy when contrasted with baseline methods across diverse models and tasks. Budgeted batch classification evaluation on MSDNet demonstrates that DFS uses about 2x fewer average FLOPs per image to achieve the same classification accuracy as baseline methods on Cifar100.