A fully nanoporous Fe-rich alloy, prepared by selective dissolution of melt-spun Fe43.5Cu56.5 ribbons, exhibits outstanding properties as a heterogeneous Fenton catalyst toward the degradation of methyl orange (MO) in aqueous solution. In addition, the ferromagnetic characteristics of this material enable its wireless manipulation toward specific locations within polluted wastewater. The influence of selective dissolution on the microstructure, sample morphology (surface and cross-section), elemental composition, and magnetic properties of the resulting nanoporous alloy is investigated. The dealloying procedure enhances the saturation magnetization and drastically increases the catalytic performance (i.e., the time required for full degradation of MO from the medium is reduced by a factor of approximately 2 by subjecting the Fe43.5Cu56.5 ribbons to prior dealloying). Remarkably, the effectiveness of this nanoporous material surpasses the results obtained by the homogeneous Fenton reaction using an equivalent concentration of Fe cations leached into the media from the nanoporous alloy. The different factors that promote the high catalytic activity are discussed. The outstanding catalytic activity, together with the simplicity of the synthetic procedure, makes this material very appealing for water remediation using advanced Fenton processes.