Meiosis is a highly specialized cell division that requires significant reorganization of the canonical cell-cycle machinery and the use of meiosis-specific cell-cycle regulators. The anaphase-promoting complex (APC) and a conserved APC adaptor, Cdc20 (also known as Fzy), are required for anaphase progression in mitotic cells. The APC has also been implicated in meiosis, although it is not yet understood how it mediates these non-canonical divisions. Cortex (Cort) is a diverged Fzy homologue that is expressed in the female germline of Drosophila, where it functions with the Cdk1-interacting protein Cks30A to drive anaphase in meiosis II. Here, we show that Cort functions together with the canonical mitotic APC adaptor Fzy to target the three mitotic cyclins (A, B and B3) for destruction in the egg and drive anaphase progression in both meiotic divisions. In addition to controlling cyclin destruction globally in the egg, Cort and Fzy appear to both be required for the local destruction of cyclin B on spindles. We find that cyclin B associates with spindle microtubules throughout meiosis I and meiosis II, and dissociates from the meiotic spindle in anaphase II. Fzy and Cort are required for this loss of cyclin B from the meiotic spindle. Our results lead to a model in which the germline-specific APC(Cort) cooperates with the more general APC(Fzy), both locally on the meiotic spindle and globally in the egg cytoplasm, to target cyclins for destruction and drive progression through the two meiotic divisions.