Miniature buckling-restrained braces (BRBs) have a concise configuration and clear working mechanism. Owing to stable and full hysteresis, miniature BRBs are emerging as favorable energy-dissipating fuse elements in seismic applications. This paper proposes using iron-shape memory alloy (FeSMA) in lieu of conventional steel as the yielding core and focuses on the cyclic behavior. Four specimens, corresponding to four loading protocols, were fabricated and tested. According to experimental data, the miniature FeSMA BRBs exhibited full hysteresis, which is characterized by large damping, noticeable isotropic and kinematic hardening behavior and appreciable post-yield stiffness ratio. The cumulative plastic deformations meet the requirement by ANSI/AISC 341-16. Further, high fidelity finite element models, which explicitly considered damage and fracture rules, were established for numerical simulations. Good agreement can be found between the experimental data and numerical simulations, in terms of failure modes, fracture locations and global hysteresis.