Originally isolated from natural products, camptothecin (CPT) has provided extensive playing fields for the development of antitumor drugs. Two of the most successful analogs of CPT, topotecan and irinotecan, have been approved by the FDA for the treatment of colon cancer and ovarian cancer, as well as other cancers. However, the emergence of drug resistance mutations in topoisomerase I is a big challenge for the effective therapy of these drugs. Therefore, in this study, a series of computational approaches from molecular dynamics (MD) simulations to steered molecular dynamics (SMD) simulations and Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) binding free energy calculations were employed to uncover the molecular principle of the topotecan resistance induced by three mutations in DNA topoisomerase I, including E418K, G503S, and D533G. Our results demonstrate a remarkable correlation between the binding free energies predicted by MM/GBSA and the rupture forces computed by SMD, and moreover, the theoretical results given by MM/GBSA and SMD are in excellent agreement with the experimental data for ranking the inhibitory activities: WT > E418K > G503S > D533G. In order to explore the drug resistance mechanism that underlies the loss of the binding affinity of topotecan, the binding modes of topotecan bound to the WT and mutated receptors were presented, and comparisons of the binding geometries and energy contributions on a per residue basis of topotecan between the WT complex and each mutant were also discussed. The results illustrate that the mutations of E418K, G503S, and D533G have great influence on the binding of topotecan to topoisomerase I bound with DNA, and the variations of the polar interactions play critical roles in the development of drug resistance. The information obtained from this study provides useful clues for designing improved topoisomerase I inhibitors for combating drug resistance.