Data acquired from multichannel sensors are a highly valuable asset to interpret the environment for a variety of remote sensing applications. However, low spatial resolution is a critical limitation for previous sensors, and the constituent materials of a scene can be mixed in different fractions due to their spatial interactions. Spectral unmixing is a technique that allows us to obtain the material spectral signatures and their fractions from hyperspectral data. In this paper, we propose a novel endmember extraction and hyperspectral unmixing scheme, so-called EndNet, that is based on a two-staged autoencoder network. This well-known structure is completely enhanced and restructured by introducing additional layers and a projection metric [i.e., spectral angle distance (SAD) instead of inner product] to achieve an optimum solution. Moreover, we present a novel loss function that is composed of a Kullback-Leibler divergence term with SAD similarity and additional penalty terms to improve the sparsity of the estimates. These modifications enable us to set the common properties of endmembers, such as nonlinearity and sparsity for autoencoder networks. Finally, due to the stochastic-gradient-based approach, the method is scalable for large-scale data and it can be accelerated on graphical processing units. To demonstrate the superiority of our proposed method, we conduct extensive experiments on several well-known data sets. The results confirm that the proposed method considerably improves the performance compared to the state-of-the-art techniques in the literature.