An efficient one-pot three-component [3 + 2]-cycloaddition reaction of azomethine ylides, generated in situ from isatins and azetidine-2-carboxylic acid, with different maleimides and itaconimides has been investigated. These reactions afford the corresponding spiro and dispiro[1-azabicyclo[3.2.0]heptanes] in moderate to high yields (up to 93%) with moderate to excellent diastereoselectivities and excellent regioselectivities under mild conditions. The method provides a simple route to the stereoselective synthesis of new polyheterocyclic systems such as 3-spiro[1-azabicyclo[3.2.0]heptane]oxindoles spiro-conjugated or fused to a succinimide moiety. The observed diastereo- and regioselectivity of cycloaddition reactions is reasoned by DFT studies. The antiproliferative effect of the synthesized compounds against cancer cell lines was assessed.