Here, we have presented a new method of 1,1,3-triglycidyloxypropane (TGP) synthesis and investigated how cross-linker branching affects mechanical properties and cytotoxicity of chitosan scaffolds in comparison with those cross-linked using diglycidyl ethers of 1,4-butandiol (BDDGE) and poly(ethylene glycol) (PEGDGE). We have demonstrated that TGP is an efficient cross-linker for chitosan at a subzero temperature at TGP:chitosan molar ratios from 1:1 to 1:20. Although the elasticity of chitosan scaffolds increased in the following order of the cross-linkers PEGDGE > TGP > BDDGE, TGP provided cryogels with the highest compressive strength. Chitosan-TGP cryogels have shown low cytotoxicity for colorectal cancer HCT 116 cell line and supported the formation of 3D multicellular structures of the spherical shape and size up to 200 µm, while in more brittle chitosan-BDDGE cryogel this cell culture formed epithelia-like sheets. Hence, the selection of the cross-linker type and concentration for chitosan scaffold fabrication can be used to mimic the solid tumor microenvironment of certain human tissue, control matrix-driven changes in the morphology of cancer cell aggregates, and facilitate long-term experiments with 3D tumor cell cultures.