One of the promises of synthetic materials in cell culturing is that control over their molecular structures may ultimately be used to control their biological processes. Synthetic polymer hydrogels from polyisocyanides (PIC) are a new class of minimal synthetic biomaterials for three-dimensional cell culturing. The macromolecular lengths and densities of biofunctional groups that decorate the polymer can be readily manipulated while preserving the intrinsic nonlinear mechanics, a feature commonly displayed by fibrous biological networks. In this work, we propose the use of PIC gels as cell culture platforms with decoupled mechanical inputs and biological cues. For this purpose, different types of cells were encapsulated in PIC gels of tailored compositions that systematically vary in adhesive peptide (GRGDS) density, polymer length, and concentration; with the last two parameters controlling the gel mechanics. Both cancer and smooth muscle cells grew into multicellular spheroids with proliferation rates that depend on the adhesive GRGDS density, regardless of the polymer length, suggesting that for these cells, the biological input prevails over the mechanical cues. In contrast, human adipose-derived stem cells do not form spheroids but rather spread out. We find that the morphological changes strongly depend on the adhesive ligand density and the network mechanics; gels with the highest GRGDS densities and the strongest stiffening response to stress show the strongest spreading. Our results highlight the role of the nonlinear mechanics of the extracellular matrix and its synthetic mimics in the regulation of cell functions.