Easy-to-handle N-hydroxyacridinecarbimidoyl chloride hydrochlorides were synthesized as convenient nitrile oxide precursors in the preparation of 3-(acridin-9/2-yl)isoxazole derivatives via 1,3-dipolar cycloaddition with terminal alkynes, 1,1-dichloroethene, and acrylonitrile. Azirines with an acridin-9/2-yl substituent attached directly or via the 1,2,3-triazole linker to the azirine C2 were also synthesized. The three-membered rings of the acridine–azirine hybrids were found to be resistant to irradiation in the UV/visible boundary region, despite their long-wave absorption at 320–420 nm, indicating that the acridine moiety cannot be used as an antenna to transfer light energy to generate nitrile ylides from azirines for photoclick cycloaddition. The acridine–isoxazole hybrids linked at the C9–C3 or C2–C3 atoms under blue light irradiation underwent the addition of such hydrogen donor solvents, such as, toluene, o-xylene, mesitylene, 4-chlorotoluene, THF, 1,4-dioxane, or methyl tert-butyl ether (MTBE), to the acridine system to give the corresponding 9-substituted acridanes in good yields. The synthesized acridine–azirine, acridine–isoxazole, and acridane–isoxazole hybrids exhibited cytotoxicity toward both all tested cancer cell lines (HCT 116, MCF7, and A704) and normal cells (WI-26 VA4).