Signal peptides and transit peptides are essential for directing mature proteins to their proper cellular locations, particularly through cleavage following transport. Although various prediction tools achieve strong performance in identifying and classifying targeting peptides, their accuracy in determining cleavage sites remains limited. We introduce DeepMaT, a deep learning model that integrates Mamba2 and a multihead self-attention mechanism, leveraging the global modeling capabilities of Mamba2 and the localized focus of self-attention. Experimental results show that DeepMaT significantly outperforms state-of-the-art models in cleavage site prediction, achieving an accuracy of 0.867 for thylakoid transit peptides and also performing well on other peptides. Moreover, DeepMaT can accurately learn the amino acid distribution of real samples. Ablation experiments show that the combination of Mamba and attention mechanisms can improve model efficiency, further proving the effectiveness of the combination. It also enables prediction of targeting peptides with unspecified cleavage sites, offering a valuable tool for protein database annotation. DeepMaT is freely available on GitHub at https://github.com/qianmao2001/DeepMaT.