3D-core sandwich composites are novel lightweight construction materials being used heavily in defense, aerospace, marine, and automobile industries. In spite of the many commendable advantages, the 3D-core sandwich composite structures are prone to barely visible low-speed impact damages that may significantly jeopardize the safety and integrity of the structural assembly. The aim of this paper is to develop an advanced structural health monitoring framework to efficiently identify such damages in the sandwich structure using ultrasonic guided wave propagation. Theoretical analysis, numerical simulations and laboratory experiments of guided wave propagation in 3DCSCS have been carried out to demonstrate the effectiveness of the identification of barely visible impact damages. It is found that the presence of such damage regions significantly magnifies the fundamental antisymmetric mode of the propagating signals. The 3D numerical simulation gives physical insight and a good agreement has been observed with experimental results which affirms our understanding of the effect of damage on the propagating waves. The impact damage regions in the sandwich structure are experimentally identified using a modified signal difference algorithm based health monitoring framework. The proposed structural monitoring framework is found to be significantly efficient for the detection of impact damages in a sandwich structure.