The development of green methods using plant extracts to synthesize bimetallic oxide nanoparticles has gained significance over the conventional physicochemical methods. The current study attempts to prepare amorphous iron–copper mixed oxide nanoparticles (As–FeCu MONPs) through green synthesis using the leaf extract of Andrographis serpyllifolia Wight as a reducing and stabilizing agent and ferrous sulphate (FeSO4.7H2O), copper sulphate (CuSO4.5H2O) as precursors. The UV-visible and FTIR spectra confirmed the formation of As–FeCu MONPs and the presence of phytochemical capping. XRD, SEM, EDAX, and DLS studies revealed the aggregation of amorphous FeCu MONPs. HRTEM, XPS, and ICP-MS analyses revealed the presence of amorphous Fe─Cu mixed oxide nanoparticles composed of spherical to irregular particles with an average diameter of approximately 15–20 nm. The good DPPH and ABTS radical- scavenging abilities of As–FeCu MONPs demonstrated their strong antioxidant potential. Moreover, the biogenic As–FeCu MONPs showed strong anti-Alzheimer’s and anti-diabetic activities by inhibiting target enzymes with IC50 values in the microgram range. Altogether, these results demonstrate that the green synthesis of As–FeCu MONPs is a remarkable strategy for producing stable amorphous iron–copper mixed oxide nanoparticles with notable in vitro enzyme inhibitory and antioxidant activities, highlighting their potential for further biological investigations.