SAT-based Bounded Model Checking (BMC) is promising for automated generation of directed tests. Due to the state space explosion problem, SAT-based BMC is unsuitable to handle complex properties with large SAT instances or large bounds. In this paper, we propose a framework to automatically scale down the SAT falsification complexity by utilizing the decision ordering based learning from decomposed sub-properties. Our framework makes three important contributions: i) it proposes learning-oriented decomposition techniques for complex property falsification, ii) it proposes an efficient approach to accelerate the complex property falsification using the learning from decomposed sub-properties, and iii) it combines the advantages of both property decomposition and property clustering to reduce the overall test generation time. The experimental results using both software and hardware benchmarks demonstrate the effectiveness of our framework.