We study the classical multi-stage stochastic decision problem, wherein the exact distribution of uncertainty remains unknown. To measure the distributional uncertainty over the entire planning horizon, an ambiguity set defined by a probability distance metric is adopted and the problem is modeled within the conventional framework of distributionally robust optimization. We use Kullback-Leibler divergence as the underlying probability distance metric and demonstrate that solving such a problem is computationally demanding. Then, we introduce the robust satisficing framework which employs a target-driven approach to encompass all possible probability distributions. Under this framework, we show that the multi-stage stochastic decision problem can be reformulated into a series of dynamic programming problems, and the optimal policy can be determined through a Bellman-type backward induction. Additionally, we extend the analysis from KL-divergence to the general utility-based probability distance and yield analogous theoretical results. Later, we apply our approach to two different operation management problems: joint inventory-pricing problem and capacity expansion problem. In these two applications, we illustrate the optimality of base-stock policy under the robust satisficing framework. Finally, through our numerical results, we show the promising performance of our approach in effectively addressing uncertain scenarios and achieving predefined target.