The increasing frequency of natural disasters imposes severe social and economic impacts, while real-world relief operations are often constrained by both demand uncertainty and budget limitations, leading to frequent misjudgments in prepositioning and post-disaster allocation. To address this, a two-stage robust optimization (TSRO) model is developed for disaster relief network design in the preparedness–response setting, jointly optimizing facility activation, resource prepositioning, and post-disaster transportation under budget constraints. The objective is to minimize the total cost of activation, storage, and transportation, supported by a rigorously defined demand uncertainty set. To enhance tractability, we employ a column-and-constraint generation (C&CG) decomposition algorithm and incorporate KKT-based reformulation to achieve efficient solution of large-scale instances. A case study on Typhoon “Ma-on” demonstrates that the model identifies cost-effective repository portfolios and feasible allocation plans, significantly controlling total costs while satisfying worst-case demand. Sensitivity analysis on demand further provides quantitative guidance for inventory prepositioning and corridor protection. The framework delivers staged, interpretable decision support for budget-constrained humanitarian operations.