Several new amino-substituted aza-acridine derivatives bearing a basic side chain have been designed and synthesized. The antiproliferative activity of the target compounds has been evaluated against three cancer cell lines—namely HCT-116 (colorectal), the uterine sarcoma MES-SA, and its doxorubicin-resistant variant MES-SA/Dx5. A limited number of the new acridines showed marginal cytotoxicity against the tested cell lines; nevertheless, these analogues possessed a similar substitution pattern. The moderate biological activity of these derivatives was attributed to their instability in aqueous media, which has been studied by mass spectrometry and computational chemistry experiments at the density functional level of theory (DFT).