Bioremediation via floating treatment wetlands/islands (FTW/I) is a sustainable, upcoming strategy to clean over-fertilized waters. Heavy metal pollution could be addressed in the same system. For implementing this feature, heavy-metal-adsorbing filter papers were prepared in a scalable procedure. Polyamine-functionalized papers based on the grafting of polyethyleneimine (PEI) and chitosan were prepared in aqueous immersion baths and tested for their heavy metal adsorption capability. Compared to untreated cellulose, the prepared filter papers exhibited great heavy metal reduction in a filtration setup. Compellingly, the natural biopolymer functionalization with chitosan adsorbed similar or even higher amounts (80% Ni, 65% Co, 100% Cu, 85% Fe, 40% Cr, 90% Cd, and 66% Zn of the 5 ppm heavy metal sulfate solutions) compared to the PEI filters (48% Ni, 36% Co, 89% Cu, 96% Fe, 45% Cr, 84% Cd, and 62% Zn) at pH 6.5. Moreover, the filters can be re-used simply by acidic washing to desorb the heavy metals, which was demonstrated in five repeating cycles. The presented chitosan–cellulose papers were prepared from renewable resources in a 3-step production lane and are a sustainable choice for various heavy-metal-removing applications. The papers can be implemented into floating treatment wetland systems to protect plants and microorganisms during phytoremediation processes and to add the additional feature of heavy metal removal for FTWs.