In view of the alternating change of soft and hard rock mass in the work face, physical model test and numerical simulation were conducted to investigate the dynamic response of tunnel surrounding rock during the process of TBM excavation in composite strata at the Lanzhou water source construction project. Similar composite rock mass materials with different strength ratios of surrounding rock were prepared by performing analogous proportion experiments. The fiber grating technology was used to capture the strain evolution law of surrounding rock in composite strata during tunnel excavation, and the macroscopic fracture morphology of the surrounding rock of the tunnel was also analyzed. The physical experimental results show that the variation law of strain in composite strata during the TBM propulsion process reflects the spatial effect of the face thrust. The strain of soft rock is greater than that of hard rock, and with the increase of excavation steps, the difference of strain between two rock strata becomes greater. After the excavation, the macroscopic fracture morphology of surrounding rock indicates that the deformation and failure of the overlying soft rock is more serious and significant due to the difference in physical and mechanical properties of the composite rock mass. The phenomenon of “uncoordinated deformation” can also be found at the interface between soft and hard rock layers. The geomechanical parameters of a tunnel section along the project are selected to evaluate the stability of surrounding rock in composite strata during tunnel excavation based on the failure approach index (FAI). The numerical results show that FAI changes obviously in soft rock during excavation, and the plastic zone and failure zone are more widely distributed, while the lower hard rock is less affected by excavation disturbance, and only a small range of rock mass at the arch bottom enters the failure state during excavation. Both the model test and the numerical results indicate that there are differences in change laws in the deformation and failure of the surrounding rock during the excavation process. Therefore, the construction of TBM in the composite stratum can take measures such as monitoring and early warning of key parts as well as early corresponding measures reduce or avoid the occurrence of TBM jamming accidents.