(Cu43Zr48Al9)98Y2 amorphous alloy bar was prepared by the arc melting copper mold absorption casting method, and then, the amorphous alloy was annealed at different temperatures for different times. The influence of heating rate on thermal expansion and thermal stability was studied by thermomechanical analysis (TMA), and the microstructure evolution of the amorphous alloy during structural relaxation and crystallization was studied by XRD and TEM. Results show that the structural evolution behavior of the (Cu43Zr48Al9)98Y2 amorphous alloy can be divided into five different stages (structural relaxation preparation stage, structural relaxation stage, first crystallization stage, second crystallization stage, and grain growth stage). When the heating rate is 20 K/min, the amorphous alloy has the smallest thermal expansion coefficient and the best thermal stability. The width of the supercooled liquid region is 66.42 K. Samples with different relaxation states were prepared by annealing at the heating rate of 20 K/min. The structural evolution of amorphous alloys with different relaxation states is as follows: amorphous → CuZr2 + AlCu2Zr7 → CuZr2 + AlCu2Zr7 + CuZr(B2) + CuZr(M) + Cu10Zr7 → CuZr2 + AlCu2Zr7 + CuZr(B2) + CuZr(M). After annealing at 706 K and 726 K (in the supercooled liquid region) for 1.5 h, the amorphous-nanocrystalline composites were obtained. When the annealing temperature is 706 K, the crystallization process of the sample is as follows: amorphous → Cu10Zr7 → Cu10Zr7 + CuZr, and for the sample at 726 K, it is as follows: amorphous → CuZr2 + AlCu2Zr7 + Cu10Zr7 → Cu10Zr7 + CuZr2 → CuZr2 + CuZr (B2) +Cu10Zr7.