Spheroidal cancer cell cultures have been used to enrich cancer stem cells (CSC), which are thought to contribute to important clinical features of tumors. This study aimed to map the regulatory networks driven by circular RNAs (circRNAs) in CSC-enriched colorectal cancer (CRC) spheroid cells. The spheroid cells established from two CRC cell lines acquired stemness properties in pluripotency gene expression and multi-lineage differentiation capacity. Genome-wide sequencing identified 1503 and 636 circRNAs specific to the CRC parental and spheroid cells, respectively. In the CRC spheroids, algorithmic analyses unveiled a core network of mRNAs involved in modulating stemness-associated signaling pathways, driven by a circRNA–microRNA (miRNA)–mRNA axis. The two major circRNAs, hsa_circ_0066631 and hsa_circ_0082096, in this network were significantly up-regulated in expression levels in the spheroid cells. The two circRNAs were predicted to target and were experimentally shown to down-regulate miR-140-3p, miR-224, miR-382, miR-548c-3p and miR-579, confirming circRNA sponging of the targeted miRNAs. Furthermore, the affected miRNAs were demonstrated to inhibit degradation of six mRNA targets, viz. ACVR1C/ALK7, FZD3, IL6ST/GP130, SKIL/SNON, SMAD2 and WNT5, in the CRC spheroid cells. These mRNAs encode proteins that are reported to variously regulate the GP130/Stat, Activin/Nodal, TGF-β/SMAD or Wnt/β-catenin signaling pathways in controlling various aspects of CSC stemness. Using the CRC spheroid cell model, the novel circRNA–miRNA–mRNA axis mapped in this work forms the foundation for the elucidation of the molecular mechanisms of the complex cellular and biochemical processes that determine CSC stemness properties of cancer cells, and possibly for designing therapeutic strategies for CRC treatment by targeting CSC.