This paper presents a new technique for learning category-level manipulation from raw RGB-D videos of task demonstrations, with no manual labels or annotations. Category-level learning aims to acquire skills that can be generalized to new objects, with geometries and textures that are different from the ones of the objects used in the demonstrations. We address this problem by first viewing both grasping and manipulation as special cases of tool use, where a tool object is moved to a sequence of key-poses defined in a frame of reference of a target object. Tool and target objects, along with their key-poses, are predicted using a dynamic graph convolutional neural network that takes as input an automatically segmented depth and color image of the entire scene. Empirical results on object manipulation tasks with a real robotic arm show that the proposed network can efficiently learn from real visual demonstrations to perform the tasks on novel objects within the same category, and outperforms alternative approaches.