At present, spectral clustering is an important branch of unsupervised learning, and its application in deep learning has been widely concerned. However, for high-dimensional sparse datasets, the complexity of network scale leads to parameter explosion, and static Gaussian kernel often has wrong preset data structure. To overcome these challenges, we propose a novel deep clustering model, Deep Clustering Based on Sparse Kolmogorov-Arnold Network (KAN) and Spectral Constraint. It contains a deep sparse clustering framework, in which sparse KAN and the orthogonal layer are designed to enhance the sparsity of the activation function matrix, reduce the number of parameters and improve the stability of model convergence. Additionally, we add an adaptive optimized affinity matrix based on spectral constraint, which overcomes the limitations of static Gaussian kernels, and improves the performance and stability of spectral constraint. Experimental results on both synthetic and real datasets demonstrate that our model outperforms existing methods in clustering performance, computational efficiency, and stability.