We design a greedy routing scheme specifically for GPS-free large-scale wireless sensor networks deployed on surfaces of complex-connected three-dimensional settings. Compared with other greedy embedding–based surface network routing scheme, the proposed one is cut free such that no pair of nodes suffers a long detour to reach each other. The routing scheme is designed to be resilient to node or link failures especially under random node or link failure model where each node in a network has an equal and independent probability of failure during some time interval. The proposed algorithm is fully distributed and scalable to both the size and the topological complexity of a network. Each sensor node requires only limited and constant storage. Simulation results show the proposed routing scheme with a higher successful delivery ratio, a lower average stretch factor, and a lower normalized communication cost compared with other resilient routing methods.