SVG (Scalable Vector Graphics) is a widely used graphics format that possesses excellent scalability and editability. Image vectorization that aims to convert raster images to SVGs, is an important yet challenging problem in computer vision and graphics. Existing image vectorization methods either suffer from low reconstruction accuracy for complex images or require long computation time. To address this issue, we propose SuperSVG, a superpixel-based vectorization model that achieves fast and high-precision image vectorization. Specifically, we decompose the input image into superpixels to help the model focus on areas with similar colors and textures. Then, we propose a two-stage self-training framework, where a coarse-stage model is employed to reconstruct the main structure and a refinement-stage model is used for enriching the details. Moreover, we propose a novel dynamic path warping loss to help the refinement-stage model to inherit knowledge from the coarse-stage model. Extensive qualitative and quantitative experiments demonstrate the superior performance of our method in terms of reconstruction accuracy and inference time compared to state-of-the-art approaches.