The prohibitive complexity of convolutional neural networks (CNNs) has triggered an increasing demand for network simplification. To this end, one natural solution is to remove the redundant channels or layers to explore simplified network structures. However, the resulting simplified network structures often suffer from suboptimal accuracy-efficiency tradeoffs. To overcome such limitations, we, in this work, introduce a simple yet effective network simplification approach, namely Domino, which aims to comprehensively revisit the tradeoff dilemma between accuracy and efficiency from a new perspective of linearity and nonlinearity through linearity grafting. Furthermore, we also draw insights from Domino and introduce two enhanced variants, namely Domino-Pro and Domino-Pro-Max, to improve the attainable accuracy on target task without degrading the runtime efficiency on target hardware. Extensive experiments are conducted on two popular Nvidia Jetson embedded hardware systems (i.e., Xavier and Nano) and two representative deep convolutional networks (i.e., MobileNetV2 and ResNet50), which clearly demonstrate the superiority of Domino and its two enhanced variants over previous state-of-the-art methods.