The research on amorphous metal-organic frameworks (aMOFs) is still in its infancy, and designing and constructing aMOFs with functional pores remains a challenge. Two aMOFs based on Co(II) and heterotopic triangular ligands with large conjugated aromatic planes, namely aMOF-1 and aMOF-2, were constructed and characterized by IR, XPS, EA, ICP, XANS and so on. aMOF-1 possesses mesopores, whereas aMOF-2 possesses micropores. The porosity, conjugated aromatic plane and uncoordinated N atoms in the framework allow these aMOFs to adsorb iodine and dyes. The iodine adsorption capacity of aMOF-1 is 3.3 g per g, which is higher than that of aMOF-2 (0.56 g per g), mainly due to the expansion or swelling of aMOF-1 after iodine adsorption. The uptake of cationic dyes by aMOF-2 showed more rapid kinetics and a higher removal rate than that by aMOF-1, mainly due to the difference in the porosity and surface charge. Although the surface charges of aMOF-1 and aMOF-2 are negative, both of them showed significantly faster adsorption kinetics toward anionic dyes, among which methyl orange (MO) and Congo red (CR) can be removed in 5 min. This occurs possibly because the quick adsorption of Na+ ions alters the surface charge of the framework and promotes dye uptake. The adsorption capacities of aMOF-1 for MO and CR reached 921 and 2417 mg g-1, respectively. The correlation data for aMOF-2 are 1042 and 1625 mg g-1, respectively. All adsorption capacities are among the highest compared to many cMOFs. Adsorption in mixed dye solution is found to be charge-dependent, kinetic-dependent, and synergetic in these systems. The porosity, surface charge regulation during adsorption, weak interactions and multiple adsorption processes contribute to the dye adsorption performance.