Steroid dimers of natural and synthetic origin possess an unusual and complex molecular architecture that may lead to the realization of peculiar effects in biological systems, in particular in different cancer cell lines. In the present work, diastereoselective ring-opening of mono- and polyoxiranes, containing a cyclooctane core, by azide-anion was performed to yield a series of azidoalcohols with different types of symmetry. The products were involved in copper-catalyzed azyde-alkyne cycloaddition (CuAAC) reaction with ethinylestradiol and ethinyltestosterone, and the resulting steroids and steroid dimers with triazole linkers were screened for their antiproliferative activity via (3-(4,5-dimethylthiazol-2-yl)2,5-diphenyl tetrazolium bromide) assay. All the compounds revealed cytotoxicity toward several cancer cell lines. The effect of the most potent compound, containing two estradiol moieties, on the microtubules (MT) dynamics was investigated by immunofluorescent microscopy. The disruption of the majority of interphase cell cytoplasmic MT and mitotic event disturbances in the presence of the studied compound were observed. The latter effect caused the appearance of numerous multinucleated cells.