The dynamic processes, of energy transfer of the 4T1 exciton of Mn2+ ions have been studied in the temperature region 2-300 K in the pure and Mg2+-, Ni2+-, Co2+-doped quasi-one-dimensional antiferromagnet CsMnCl3·2D2O (CMC). It has been found that the fluorescent intensity and the lifetime of the exciton drops rapidly with increasing temperature in the region 2-10 K, with a further weakened fluorescence and shortened lifetime in the heavily doped crystals. These phenomena are presumed to be associated with the multiphonon nonradiative transition and energy transfer between donors and acceptors, both of which are related to the magnetic interactions and the spin ordering. At higher temperature, the rate of energy transfer increases. However, because of the persistence of spin short-range order and the Jahn-Teller effect, the energy transfer among donors is still limited to some extent, and nonexponential attenuation processes appear. The different impurities show different abilities of trapping and relaxing to a certain degree.