In this study, magnetorheological elastomers (MREs) based on iron sand and natural rubber were prepared. The Taguchi method was employed to investigate the effect of a number of factors, namely, the iron sand content, iron sand particle size, and applied magnetic field during curing on the loss tangent (tan δ) and energy dissipated during cyclic loading. Tan δ was measured through dynamic mechanical analysis over a range of frequency (0.01–130 Hz), strain amplitude (0.1–4.5%), and temperature (−100 to 50°C). The energy dissipated was measured with a universal tester under cyclic tensile loading. The data were then statistically analyzed to predict the optimal combination of factors, and finally, experiments were conducted for verification. It was found that the iron sand content had the greatest influence on tan δ when measured over a range of frequency, and the energy dissipated during hysteresis tests. However, none of the factors showed a significant influence on tan δ when measured over a range of strain amplitude. Furthermore, the iron sand content and magnetic field were also found to influence the width of the peak in tan δ as a function of the temperature. The morphological characteristics of the MREs were also examined with scanning electron microscopy.