To study the influence of mineral admixtures on concrete’s mechanical properties after a low-temperature exposure, green concrete was prepared by mixing fly ash and slag at different replacement rates. By analysing the changes to concrete’s mechanical properties and the damage layer thickness under different ambient temperatures (20, −10, −20, −30, and −40 °C), the change rule of concrete at low temperatures was explored. The results revealed that the compressive strength of concrete, containing either fly ash or slag, peaked at 30 °C; moreover, the slag concrete’s flexural and splitting tensile strength peaked at −40 °C. The best mechanical properties were observed for a fly ash-to-slag ratio of 1:2 (F10S20; i.e., 10% fly ash and 20% slag) and its compressive strength at different temperatures was higher than that of concrete, containing 30% fly ash (F30) or 30% slag (S30), but the flexural and splitting tensile strength was lower than S30. Further, as the temperature decreased, the fly ash concrete’s damaged layer thickness gradually increased. When the content of fly ash and slag were both 15% (F15S15), the damaged layer thickness was minimal at different low temperatures, especially at −30 °C, where the thickness was only 8.31 mm.