Few studies have focused on the advanced oxidation processes (AOPs) based on heterogeneous catalysis to control harmful algal blooms (HABs). Herein, a mesoporous carbon framework supported Fe-Cu-Mn oxides (MnFe2O4/CuO; FCMT) was synthesized via calcination of cost-effective metal-polyphenol coordination polymers for peroxymonosulfate (PMS) activation to eliminating Microcystis aeruginosa and algal organic matters (AOMs). >99% of algae were removed at low FCMT and PMS dosages in the FCMT/PMS within 120 min. The FCMT/PMS system removed algae effectively over extensive pH (3.0–9.0) and algal density (OD680 = 0.05–0.4) ranges. Although FCMT/PMS-induced oxidative stress damaged cell membranes, over 50% of the dissolved organic carbon and 54% of microcystins were eliminated, avoiding serious secondary pollution caused by cell lysis. Algal removal by the FCMT/PMS system involved pathways associated with both free radicals and non-free radicals, with the dominant reactive oxygen species being O2− and 1O2. Synergy between Fe, Mn, and Cu promoted the elimination of algae and AOMs. Mn found to be the primary active site on the FCMT surface, while Fe(III) was cooperated with Mn by acting as the main adsorption site. The mesoporous carbon allowed uniform spatial distribution of the nanosized Fe-Cu-Mn oxides as well as modulating the direction of reactive oxygen species generation by the metals. In conclusion, the proposed heterogeneous advanced oxidation process using the FCMT/PMS system is highly potential in the control of HABs.