Supramolecular hydrogels utilizing host-guest interactions (HG gels) exhibit large deformability and pronounced viscoelasticity. The inclusion complexes between β-cyclodextrin (host) and adamantane (guest) units on the water-soluble polymers form transient bonds. The HG gels show significant stress relaxation with finite equilibrium stress following the step strain. The stress relaxation process reflects the detachment dynamics of the transient bonds which sustain the initial stress, while the finite equilibrium stress is preserved by the permanent topological cross-links with a rotaxane structure. Nonlinear stress relaxation experiments in biaxial stretching with various combinations of two orthogonal strains unambiguously reveal that time and strain effects on stress are not separable. The relaxation is accelerated for a short time frame (<102 s) with an increase in the magnitude of strain, whereas it is retarded for a longer time window with an increase in the anisotropy of the imposed biaxial strain. The time-strain inseparability in the HG gels is in contrast to the simple nonlinear viscoelasticity of a dual cross-link gel with covalent and transient cross-links in which the separability was previously validated by the same assessment. We currently interpret that the significant susceptibility of the detachment dynamics to the deformation type results from the structural characteristics of the HG gels, i.e., the host and guest moieties covalently connected to the network chains, the considerably low concentrations (<0.1 M) of these moieties, and the slidability of the permanent rotaxane cross-links.