Cloud manufacturing is characterized by large uncertainties and disturbances due to its networked, distributed, and loosely coupled features. To target the problem of frequent cloud resource node failure, this paper proposes (1) three resource substitution strategies based on node redundancy and (2) a new robustness analysis method for cloud manufacturing systems based on a combination of the complex network and multi-agent simulation. First, a multi-agent simulation model is constructed, and simulation evaluation indexes are designed to study the robustness of the dynamic cloud manufacturing process (CMP). Second, a complex network model of cloud manufacturing resources is established to analyze the static topological robustness of the cloud manufacturing network. Four types of node failure modes are defined, based on the initial and recomputed topologies. Further, three resource substitution strategies are proposed (i.e., internal replacement, external replacement, and internal–external integration replacement) to enable the normal operation of the system after resource node failure. Third, a case study is conducted for a cloud manufacturing project of a new energy vehicle. The results show that (1) the proposed robustness of service index is effective at describing the variations in CMP robustness, (2) the two node failure modes based on the recalculated topology are more destructive to the robustness of the CMP than the two based on the initial topology, and (3) under all four failure modes, all three resource substitution strategies can improve the robustness of the dynamic CMP to some extent, with the internal–external integration replacement strategy being most effective, followed by the external replacement strategy, and then the internal replacement strategy.