The fusion of hyperspectral and multispectral images is an important strategy for enhancing the spatial resolution of hyperspectral images. With the rapid advancement of multispectral imaging technology, the disparity in spatial resolution between multispectral and hyperspectral images is increasing. In certain scenarios, termed high-magnification, this difference can exceed $32\times$ . Previous methods do not perform well under high-magnification fusion, and naturally, a challenge arises in achieving effective high-magnification super-resolution fusion. In light of the above analysis, this article introduces a novel algorithm for high-magnification super-resolution fusion of hyperspectral and multispectral images based on the joint optimization of spatial and spectral information. Specifically, our algorithm consists of three stages: 1) a fast preliminary fusion stage based on the Moore-Penrose inverse and singular value correlation priors for the rapid acquisition of preliminary solutions; 2) a joint spatial-spectral optimization stage where a coupled optimization framework is constructed to achieve integrated optimization of spatial and spectral information; and 3) an error backpropagation optimization stage where an effective error optimization term is introduced to further refine the fusion performance. We conducted extensive experiments on widely employed publicly available simulated datasets and real datasets. The experimental results unequivocally indicate that our proposed methodology consistently exhibits superior fusion performance compared with state-of-the-art methods, even under the condition of ${\geq }60\times$ super-resolution.