Learning deep neural networks on human motion data has become common in computer graphics research, but the heterogeneity of available datasets poses challenges for training large-scale networks. This paper presents a framework that allows us to solve various animation tasks in a skeleton-agnostic manner. The core of our framework is to learn an embedding space to disentangle skeleton-related information from input motion while preserving semantics, which we call Skeleton-Agnostic Motion Embedding (SAME). To efficiently learn the embedding space, we develop a novel autoencoder with graph convolution networks, and we provide new formulations of various animation tasks operating in the SAME space. We showcase various examples, including retargeting, reconstruction, and interactive character control, and conduct an ablation study to validate design choices made during development.