All-perovskite-based polycrystalline thin-film tandem solar cells have the potential to deliver efficiencies of > 30%. However, the performance of all-perovskite-based tandem devices have been limited by the lack of high-efficiency, low-band-gap Sn-Pb mixed-perovskite solar cells (PSCs). We report on using guanidinium thiocyanate (GuaSCN) to dramatically improve the structural and optoelectronic properties of Sn-Pb mixed, low-band-gap (~1.25 electron volt) perovskite films that have 10-times lower defect density, leading to carrier lifetimes of greater than 1 microsecond and diffusion lengths of 2.5 micrometer. These improved properties enable our demonstration of >20%-efficient, 1.25-eV, low-band-gap PSCs. When combined with wider bandgap PSCs, we achieve 25%-efficient 4-terminal and 23.1%-efficient 2-terminal all-perovskite-based polycrystalline thin-film tandem solar cells.