Traffic prediction is one of the critical tasks in smart cities, and numerous scholars have proposed various new methods. Especially, the spatio-temporal graph neural networks (STGNNs), which mainly focus on modeling the spatial and temporal relationships of urban transportation data. However, these methods still face two major challenges: (1) Existing works primarily focus on representing spatial point-to-point (second-order) relationships using graphs, overlooking the complex potential higher-order relationships among nodes. (2) Current works mostly utilize recurrent neural networks, and temporal convolutional networks to represent the local temporal feature, they are unable to capture global temporal relationships. Although the attention mechanism can learn global temporal relationships, it suffers from high computational complexity. To address these issues, we propose a novel mixed-order spatio-temporal representation learning (MixSTRL) for traffic prediction. This method employs graph neural networks and hypergraph neural networks to represent spatial second-order and high-order relationships, respectively. Additionally, a squeeze and excitation mechanism is introduced to fuse the spatial second-order and high-order relationships. Furthermore, temporal convolutional networks and hypergraph neural networks are utilized to capture local and global temporal relationships, respectively with a gating mechanism employed to integrate them. The effectiveness of the MixSTRL model is experimentally validated on three real-world traffic datasets.