A positron lifetime study has been done on dielectric multilayer cavity mirrors for free-electron-laser experiments by the use of a variable-energy pulsed positron beam. A long-lived ortho-positronium component has been observed at low positron energy region, corresponding to the depth of the top amorphous SiO2 layer. The intensity of the positronium component correlates with the degradation and restoration of the mirrors. We discuss the relation between the positronium intensity and degradation mechanism of the mirrors. The present studies revealed that the slow positron lifetime technique is highly sensitive to the properties of the mirrors and is useful for the evaluation of the mirrors.