A structured dark focus is generated from a single linearly polarized circular Airy beam via the modulation of the angular spectrum with a band-stop filter. The beam is tailored to suppress the focal intensity, thereby creating the structured dark focus between the focal spot and the adjacent intensity peak. The field distributions are described using the angular spectrum representation (ASR), while the scattering of particles illuminated by the structured dark focus is solved within the framework of the generalized Lorentz-Mie theory. In particular, the expansion coefficients required for the generalized Lorentz-Mie theory are explicitly derived. The structured dark focus is shown to stably trap low-refractive-index Mie particles. Moreover, the trapping position of the structured dark focus can be effectively tuned by varing the conical angle. In addition, multiple dark foci are generated, enabling the simultaneous stable trapping of Mie particles at three distinct positions along the optical axis. These findings provide a new route for the stable optical trapping of low-refractive-index Mie particles.