Mulberry fruits (MF) contain many biologically active compounds beneficial for human health. In particular, in the literature, there are no studies on the kinetics of the freeze-drying of MF and the effect of the process temperature on the properties of dried fruits. The objective of this study was to ascertain how freeze-drying (FD) and air-drying temperature affected the kinetics of dehydration and chosen physicochemical parameters of MF. Both temperature and dehydration methods significantly influenced the drying rate and properties of MF. The Midilli model was the best fitted to the experimental data of the course of drying curves and with the lowest values of mean-square error. The highest lightness and yellowness were noted for freeze-dried fruit, whereas air-dried MF were characterized by the highest redness. An increase in drying temperature significantly changed the color of fruits and led to the degradation of L-ascorbic acid content. The highest content of L-ascorbic acid was found in fresh fruits (214 ± 4 mg/100 g dry mass (DM)) and freeze-dried fruits at 30 °C (182 ± 3 mg/100 g DM). Both FD and AD drying significantly reduced the content of this compound. The lowest reduction in L-ascorbic acid was observed for freeze-dried fruits. Fruits freeze-dried at 30 °C showed the highest content of total phenolics and antioxidant capacity.