Networks are ubiquitous in many real-world applications (e.g., social networks encoding trust/distrust relationships, correlation networks arising from time series data). While many networks are signed or directed, or both, there is a lack of unified software packages on graph neural networks (GNNs) specially designed for signed and directed networks. In this paper, we present PyTorch Geometric Signed Directed (PyGSD), a software package which fills this gap. Along the way, we evaluate the implemented methods with experiments with a view to providing insights into which method to choose for a given task. The deep learning framework consists of easy-to-use GNN models, synthetic and real-world data, as well as task-specific evaluation metrics and loss functions for signed and directed networks. As an extension library for PyG, our proposed software is maintained with open-source releases, detailed documentation, continuous integration, unit tests and code coverage checks. The GitHub repository of the library is https://github.com/SherylHYX/pytorch_geometric_signed_directed.