A three-component organocatalytic reaction of 1,3-dipolar cycloaddition between the in situ generated azomethine ylides and 3-substituted 1,2-diphenylcyclopropenes is described. The azomethine ylides have been generated via condensation of aromatic compounds (such as isatins and acenaphthenequinone) with benzylamines. The reaction has afforded derivatives of 3-azabicyclo[3.1.0]hexane, spiro-fused with the fragments of 2-oxindole and acenaphthylene-1(2H)-one. The cycloadducts have been obtained with yield up to 91 mainly as individual diastereomers. The influence of bifunctional squaramide-based organocatalysts on the course of these three-component reactions has been investigated. Antiproliferative activity of selected synthesized compounds with respect to the human erythromyelosis (K562) and melanoma (Sk-mel-2) cell lines has been assessed in vitro by means of MTS analysis.