Deep unrolling-based snapshot compressive imaging (SCI) methods, which employ iterative formulas to construct interpretable iterative frameworks and embedded learnable modules, have achieved remarkable success in reconstructing 3-dimensional (3D) hyperspectral images (HSIs) from 2D measurement induced by coded aperture snapshot spectral imaging (CASSI). However, the existing deep unrolling-based methods are limited by the residuals associated with Taylor approximations and the poor representation ability of single hand-craft priors. To address these issues, we propose a novel HSI construction method named residual completion unrolling with mixed priors (RCUMP). RCUMP exploits a residual completion branch to solve the residual problem and incorporates mixed priors composed of a novel deep sparse prior and mask prior to enhance the representation ability. Our proposed CNN-based model can significantly reduce memory cost, which is an obvious improvement over previous CNN methods, and achieves better performance compared with the state-of-the-art transformer and RNN methods. In this work, our method is compared with the 9 most recent baselines on 10 scenes. The results show that our method consistently outperforms all the other methods while decreasing memory consumption by up to 80%.