As the third-generation neural network, the Spiking Neural Network (SNN) has the advantages of low power consumption and high energy efficiency, making it suitable for implementation on edge devices. More recently, the most advanced SNN, Spikformer, combines the self-attention module from Transformer with SNN to achieve remarkable performance. However, it adopts larger channel dimensions in MLP layers, leading to an increased number of redundant model parameters. To effectively decrease the computational complexity and weight parameters of the model, we explore the Lottery Ticket Hypothesis (LTH) and discover a very sparse ($\ge$90%) subnetwork that achieves comparable performance to the original network. Furthermore, we also design a lightweight token selector module, which can remove unimportant background information from images based on the average spike firing rate of neurons, selecting only essential foreground image tokens to participate in attention calculation. Based on that, we present SparseSpikformer, a co-design framework aimed at achieving sparsity in Spikformer through token and weight pruning techniques. Experimental results demonstrate that our framework can significantly reduce 90% model parameters and cut down Giga Floating-Point Operations (GFLOPs) by 20% while maintaining the accuracy of the original model.