We present a field-theoretical description of the deuteron electrodisintegration reaction $d(e,e\prime p)n$ induced by unpolarized and polarized electrons. The approach combines the Lehmann-Symanzik-Zimmermann $in(out)$ formalism with the clothed particle representation in the instant form of relativistic dynamics, providing a fully relativistic and gauge-independent framework based on the Fock-Weyl criterion. Within the method of unitary clothing transformations, one and the same transformation that generates the relativistic nucleon-nucleon interaction (the Kharkiv potential) also induces a fresh family of electromagnetic current operators. As a result, one-body and two-body (meson-exchange) currents emerge on a common footing. We compute differential cross sections and polarization observables with the inclusion of final-state interaction effects and meson-exchange current contributions and compare the results with Saclay and Jefferson Lab data as well as with earlier theoretical predictions. The role of relativistic ingredients (one- and two-body currents, Fermi-motion effects, etc.) and the interplay between them are analyzed in several kinematic regimes of the experiments at Saclay and Jefferson Lab.