Information storage is an important functionality to produce a sense-decide-respond loop in active mechanical metamaterial systems. Here, we propose a new class of mechanical metamaterials with self-powered digital information storage capability. In the so-called mechanically-responsive data storage metamaterials, data is incorporated into a set of self-recovering unit cells that form the material lattice. As the metamaterial structure is loaded, the cells in each layer generate electrical signals that are coded as binary bits to represent the stored data. We show how the proposed designs can serve as sequential access memory data storage devices, where the stored data can be accessed in a deformation sequential order under mechanical stimulations. The stiffness of the metamaterial structure can be rationally designed to create either a flexible/soft or hard data storage system. We further discuss the potential of the proposed technology to create low-cost, non-volatile, and long-term storage solutions for data storage applications.