In the present study, we continue our work related to the synthesis of 1,8-naphthalimide and carborane conjugates and the investigation of their anticancer activity and DNA-binding ability. For this purpose, a series of 4-carboranyl-1,8-naphthalimide derivatives, mitonafide, and pinafide analogs were synthesized using click chemistry, reductive amination, amidation, and Mitsunobu reactions. The calf thymus DNA (ct-DNA)-binding properties of the synthesized compounds were investigated by circular dichroism (CD), UV–vis spectroscopy, and thermal denaturation experiments. Conjugates 54–61 interacted very strongly with ct-DNA (∆Tm = 7.67–12.33 °C), suggesting their intercalation with DNA. They were also investigated for their in vitro effects on cytotoxicity, cell migration, cell death, cell cycle, and production of reactive oxygen species (ROS) in a HepG2 cancer cell line as well as inhibition of topoisomerase IIα activity (Topo II). The cytotoxicity of these eight conjugates was in the range of 3.12–30.87 µM, with the lowest IC50 value determined for compound 57. The analyses showed that most of the conjugates could induce cell cycle arrest in the G0/G1 phase, inhibit cell migration, and promote apoptosis. Two conjugates, namely 60 and 61, induced ROS production, which was proven by the increased level of 2′-deoxy-8-oxoguanosine in DNA. They were specifically located in lysosomes, and because of their excellent fluorescent properties, they could be easily detected within the cells. They were also found to be weak Topo II inhibitors.