The study of spreading in networks presents a fascinating topic with a wide array of practical applications. Various strategies have been proposed to attack or immunize networks. However, it is often not feasible or necessary to consider the entire network in the context of real-world systems. Here, we focus on a certain group of target nodes with the aim of disconnecting them from the global network structure. For instance, it becomes possible to effectively prevent the transmission of the disease to vulnerable populations, such as infants and the elderly, by isolating some specific nodes such as their caretakers during the epidemic. From this perspective of targeted avoidance, we introduce a series of target centrality indicators and apply them to segment the target nodes from the giant component of the network. Additionally, we propose a more effective iterative graph-segmentation method for targeted immunization. Our experimental findings reveal that our proposed method can substantially reduce the number of nodes required for removal when compared with the methods based on target centrality, which implies a significant cost effectiveness in isolating target nodes from the rest of the network. Finally, we verify our method on a large mobility network in the scenario of the COVID-19 pandemic, and find that our method can effectively protect the elderly by immunizing or isolating a very small group of nodes.