The selection and breeding of deep rooting and drought-tolerant varieties has become a promising approach for improving the yield and adaptability of potato (Solanum tuberosum L.) in arid and semiarid areas. Therefore, the discovery of root-development-related genes and drought tolerance signaling pathways in potato is important. In this study, we used deep-rooting (C119) and shallow-rooting (C16) potato genotypes, with different levels of drought tolerance, to achieve this objective. Both genotypes were treated with 150 mM mannitol for 0 h (T0), 2 h (T2), 6 h (T6), 12 h (T12), and 24 h (T24), and their root tissues were subjected to comparative transcriptome analysis. A total of 531, 1571, 1247, and 3540 differentially expressed genes (DEGs) in C16 and 1531, 1108, 674, and 4850 DEGs in C119 were identified in T2 vs. T0, T6 vs. T2, T12 vs. T6, and T24 vs. T12 comparisons, respectively. Gene expression analysis indicated that a delay in the onset of drought-induced transcriptional changes in C16 compared with C119. Functional enrichment analysis revealed genotype-specific biological processes involved in drought stress tolerance. The metabolic pathways of plant hormone transduction and MAPK signaling were heavily involved in the resistance of C16 and C119 to drought, while abscisic acid (ABA), ethylene, and salicylic acid signal transduction pathways likely played more important roles in C119 stress responses. Furthermore, genes involved in root cell elongation and division showed differential expression between the two genotypes under drought stress. Overall, this study provides important information for the marker-assisted selection and breeding of drought-tolerant potato genotypes.