We introduce a sample-efficient method for learning state-dependent stiffness control policies for dexterous manipulation. The ability to control stiffness facilitates safe and reliable manipulation by providing compliance and robustness to uncertainties. Most current reinforcement learning approaches to achieve robotic manipulation have exclusively focused on position control, often due to the difficulty of learning high-dimensional stiffness control policies. This difficulty can be partially mitigated via policy guidance such as imitation learning. However, expert stiffness control demonstrations are often expensive or infeasible to record. Therefore, we present an approach to learn Stiffness Control from Augmented Position control Experiences (SCAPE) that bypasses this difficulty by transforming position control demonstrations into approximate, suboptimal stiffness control demonstrations. Then, the suboptimality of the augmented demonstrations is addressed by using complementary techniques that help the agent safely learn from both the demonstrations and reinforcement learning. By using simulation tools and experiments on a robotic testbed, we show that the proposed approach efficiently learns safe manipulation policies and outperforms learned position control policies and several other baseline learning algorithms.