A series of heterocyclic compounds containing spirofused barbiturate and 3-azabicyclo[3.1.0]hexane frameworks have been studied as potential antitumor agents. Antiproliferative activity of products was screened in human erythroleukemia (K562), T lymphocyte (Jurkat), and cervical carcinoma (HeLa) as well as mouse colon carcinoma (CT26) and African green monkey kidney epithelial (Vero) cell lines. The most effective among the screened compounds show IC50 in the range from 4.2 to 24.1 μM for all tested cell lines. The screened compounds have demonstrated a significant effect of the distribution of HeLa and CT26 cells across the cell cycle stage, with accumulation of cells in SubG1 phase and induced apoptosis. It was found, using a confocal microscopy, that actin filaments disappeared and granular actin was distributed diffusely in the cytoplasm of up to 90% of HeLa cells and up to 64% of CT26 cells after treatment with tested 3-azaspiro[bicyclo [3.1.0]hexane-2,5′-pyrimidines]. We discovered that the number of HeLa cells with filopodium-like membrane protrusions was reduced significantly (from 91% in control cells to 35%) after treatment with the most active compounds. A decrease in cell motility was also noticed. Preliminary in vivo experiments on the impact of the studied compounds on the dynamics of CT26 tumor growth in Balb/C mice were also performed.