Magnetic MnO$_2$ nanocomposites with flower-like and wire-like morphologies were synthesized, characterized and well applied for degradation of methyl orange, as model acidic azo dye, from aqueous media. The characterization studies showed the successful formation of the proposed nanocomposites with desirable properties. In addition, the surface properties of the nanocomposite were enhanced by MnO$_2$ modification, creating more efficient reaction sites for dye degradation. The effects of different factors such as initial pH, dye concentration, contact time, nanocomposite dosage, stirring rate, type and amount of scavenger in degradation efficiency are investigated using experimental design. The degradation efficiencies of nanocomposites with flower-like were higher than its wire-like morphology, and under optimum conditions (i.e., pH 5, catalyst dose 1.5 g l$^{–1}$, hole scavenger 0.15% (w/v), time 30 min, dye concentration 400 ppm, under stirring rate 300 rpm) degradation efficiencies above 99% were achieved. The kinetics, isotherm and thermodynamic studies for dye degradation process using the proposed nanocomposites were perused. Negative ${\Delta}$G$^o$ confirms the spontaneous nature of the optical decolourization MO decomposition process. Finally, due to the sample fabrication method, environmental compatibility and good potential due to flower- and wire-like morphologies, the proposed nanocomposites were successfully used as adsorbent-photocatalyst for dye degradation from different real aqueous media.