The seismic behavior of (plane) frames with special-shaped concrete-filled steel tubular (CFST) columns (SCFSTFs), H-shaped steel beams, and exterior diaphragm connections was investigated experimentally and numerically in this study. Double-bay two-story SCFSTFs with a scale ratio of 1/2 were tested under constant vertical compressive load and cyclic horizontal loads (or displacements), which is a pseudo-static experiment considering the axial compression ratio. Based on the experimental results, failure modes, bearing capacity, hysteretic curves, skeleton curves, energy dissipation, ductility, rigidity degradation, and strength degradation of SCFSTFs were investigated. As a result, a typical strong column-weak beam failure mode was observed; degradation in strength and rigidity were minimal, and the energy dissipation capacity and ductility of SCFSTFs were adequate, demonstrating excellent seismic performance. Besides, energy dissipation capacity and horizontal load bearing capacity were improved with increasing axial compression ratios within the parametric range of this test. After testing, a finite element method based on ABAQUS was carried out to further investigate the seismic performance of SCFSTFs. The numerical results of skeleton curves, stiffness, yield load, ultimate load, and stress distribution agreed well with the test results. The plastic hinge formation process and failure mode were also further investigated using the finite element method.