Cyber-epidemics, the widespread of fake news or propaganda through social media, can cause devastating economic and political consequences. A common countermeasure against cyber-epidemics is to disable a small subset of suspected social connections or accounts to effectively contain the epidemics. An example is the recent shutdown of 125,000 ISIS-related Twitter accounts. Despite many proposed methods to identify such subset, none are scalable enough to provide high-quality solutions in nowadays billion-size networks. To this end, we investigate the Spread Interdiction problems that seek most effective links (or nodes) for removal under the well-known Linear Threshold model. We propose novel CPU-GPU methods that scale to networks with billions of edges, yet, possess rigorous theoretical guarantee on the solution quality. At the core of our methods is an $O(1)$-space out-of-core algorithm to generate a new type of random walks, called Hitting Self-avoiding Walks (HSAWs). Such a low memory requirement enables handling of big networks and, more importantly, hiding latency via scheduling of millions of threads on GPUs. Comprehensive experiments on real-world networks show that our algorithms provides much higher quality solutions and are several order of magnitude faster than the state-of-the art. Comparing to the (single-core) CPU counterpart, our GPU implementations achieve significant speedup factors up to 177x on a single GPU and 338x on a GPU pair.