Responsive nanogel systems are interesting for the drug delivery of bioactive molecules due to their high stability in aqueous media. The development of nanogels that are able to respond to biochemical cues and compatible with the encapsulation and the release of large and sensitive payloads remains challenging. Here, multistimuli-responsive nanogels were synthesized using a bio-orthogonal and reversible reaction and were designed for the selective release of encapsulated cargos in a spatiotemporally controlled manner. The nanogels were composed of a functionalized polysaccharide cross-linked with pH-responsive hydrazone linkages. The effect of the pH value of the environment on the nanogels was fully reversible, leading to a reversible control of the release of the payloads and a "stop-and-go" release profile. In addition to the pH-sensitive nature of the hydrazone network, the dextran backbone can be degraded through enzymatic cleavage. Furthermore, the cross-linkers were designed to be responsive to oxidoreductive cues. Disulfide groups, responsive to reducing environments, and thioketal groups, responsive to oxidative environments, were integrated into the nanogel network. The release of model payloads was investigated in response to changes in the pH value of the environment or to the presence of reducing or oxidizing agents.