Implicit neural representations (INRs) have revolutionized arbitrary-scale super-resolution (ASSR) by modeling images as continuous functions. Most existing INR-based ASSR networks first extract features from the given low-resolution image using an encoder, and then render the super-resolved result via a multi-layer perceptron decoder. Although these approaches have shown promising results, their performance is constrained by the limited representation ability of discrete latent codes in the encoded features. In this paper, we propose a novel ASSR method named GaussianSR that overcomes this limitation through 2D Gaussian Splatting (2DGS). Unlike traditional methods that treat pixels as discrete points, GaussianSR represents each pixel as a continuous Gaussian field. The encoded features are simultaneously refined and upsampled by rendering the mutually stacked Gaussian fields. As a result, long-range dependencies are established to enhance representation ability. In addition, a classifier is developed to dynamically assign Gaussian kernels to all pixels to further improve flexibility. All components of GaussianSR (i.e. encoder, classifier, Gaussian kernels, and decoder) are jointly learned end-to-end. Experiments demonstrate that GaussianSR achieves superior ASSR performance with fewer parameters than existing methods while enjoying interpretable and content-aware feature aggregations.