We develop a continuum model of the dynamic-mechanical response of vitrimers, where the elastic energy of the material accounts for the conserved number of the crosslinks in the network. We also prepare partial vitrimer networks, which consist of variable fractions of a transient network based on boronic ester bond-exchange and of a permanent polymer network. By fitting the theory to our experimental data on stress relaxation, the bond-exchange rate and the fraction of the permanent elastic network are obtained, with a linear relationship between the fraction of the transient polymer network and the ratio between the boronic ester and the flexible spacer among the chain-extending thiols. For a 100% vitrimer undergoing a ramp deformation, the stress of the material first increases and then decreases, where the yield time decreases with an increasing strain rate. A partial vitrimer can behave as a pure elastic material without yielding at low strain rates or show a nonmonotonic "S-shaped" stress-strain relationship at high strain rates.