High-performance engineered structural systems are crucial for sustainable development in the field of construction. In our previous research, a novel steel–concrete composite beam with transverse and longitudinal hidden girders exhibited good flexural behavior and desirable ductility. However, there is a dearth of studies on the flexural response of a steel–concrete composite slab voided with thin-walled core boxes. Therefore, in this study, we investigated the overarching flexural mechanism of the proposed structure when subjected to uniform vertical loads. The experimental detection results illustrated that the deflection value of the composite beam was 95.75% less than the GB/T 50152-2012 recommendation. Numerical results further validated this observation. The recorded data from the strain profile at the mid-span of the frame girder indicated that there was a considerable membrane effect, which delayed the strain growth of rebars, yielding appreciable bearing capacity. Thus, two original approaches to predicting the ultimate load of this novel structure are proposed, considering limit analysis using the upper-bound method and the membrane effect, with the latter closely linked to the experimental results. The findings can promote the extensive application of similar sustainable systems and inspire further advancements in advanced engineering structures.