Since the current off-line routing algorithms for low earth orbit (LEO)/medium earth orbit (MEO) satellite networks lack the ability of getting information on traffic distribution and link state, they can neither optimize routes nor adapt to the unpredictable topological changes. A destruction-resistant dynamic routing algorithm is proposed in this paper to solve these defects. Based on a cluster-based link-state-delivery scheme, link state information is transmitted all over the network at a low bandwidth cost; and then a border-satellite source routing scheme optimizes the routes by considering the factors like link state, routing handovers, etc. An off-line routing algorithm and the destruction-resistant dynamic routing algorithm are applied to Iridium system model for simulation. Simulation results show that in addition to the enhanced survivability, the latter's performance is better, especially when some inter-satellite links (ISLs) break down.