We present a novel freehand sketch beautification method, which takes as input a freely drawn sketch of a man-made object and automatically beautifies it both geometrically and structurally. Beautifying a sketch is challenging because of its highly abstract and heavily diverse drawing manner. Existing methods are usually confined to the distribution of their limited training samples and thus cannot beautify freely drawn sketches with rich variations. To address this challenge, we adopt a divide-and-combine strategy. Specifically, we first parse an input sketch into semantic components, beautify individual components by a learned part beautification module based on part-level implicit manifolds, and then reassemble the beautified components through a structure beautification module. With this strategy, our method can go beyond the training samples and handle novel freehand sketches. We demonstrate the effectiveness of our system with extensive experiments and a perceptive study.