Purple sweet potato (PSP) is a rich source of anthocyanins, but the anthocyanin content and color can be affected by the drying method and processing condition. Response surface methodology (RSM) with a Box–Behnken design (BBD) was used to investigate the effects of citric acid (CA) concentration, steam pressure (SP) and rotation speed (DS) on the physicochemical and functional properties of drum-dried purple sweet potato powder (PSPP). The anthocyanins of the PSPP were analyzed using mass spectrometry with electrospray ionization and twelve anthocyanins were identified. The results indicated that the moisture content (4.80 ± 0.17–9.97 ± 0.03%) and water activity (0.290 ± 0.004–0.47 ± 0.001) (p < 0.05) decreased with increasing drum temperature as well as with reduced drum rotating speed. CA had a significant (p < 0.05) effect on the color and total anthocyanin content (101.83 ± 2.20–124.09 ± 2.89 mg/100 g) of the PSPP. High SP and low DS negatively affected the antioxidant properties of the PSPP. DPPH value of the PSPP ranged from 20.41 ± 0.79 to 30.79 ± 1.00 μmol TE/g. The optimal parameters were achieved at 0.59% CA, 499.8 kPa SP and 3 rpm DS.