This study investigates the flexural performance and degree of composite action (DCA) of precast concrete sandwich panels (PCSPs) with four types of connectors. Five full-scale specimens were designed, and 4-point bending tests were performed. The specimens included four PCSPs utilizing glass fiber reinforced polymer (GFRP) truss connectors, steel truss connectors, concrete rib connectors, and GFRP pin connectors, respectively, along with a solid panel (SP). The results indicated that the flexural performance and DCA provided by the four types of connectors followed an ascending order as follows: GFRP pin-type connectors, GFRP truss connectors, steel truss connectors, and concrete rib-type connectors. Moreover, the study presented a novel method for calculating DCA, namely, the neutral axis method, which was compared with the displacement and strain methods. The reasonableness and accuracy of the neutral axis method in calculating DCA during the linear elastic stage were verified. Results indicated that the neutral axis method provided more precise and reasonable DCA that closely matched the experimental results compared with the displacement and strain methods. Additionally, the neutral axis method was simpler to calculate DCA and had a broader range of applications. Finally, the study provided recommendations for the optimal application scenarios of each calculation method.