We study the electron-impact dissociative ionization of ${\mathrm{SF}}_{6}$ using a scattered electron-ion coincidence technique. The ion-yield spectra are obtained at an incident electron energy of 1.4 keV for scattering angles ranging from $2.{2}^{\ensuremath{\circ}}$ to $8.{2}^{\ensuremath{\circ}}$ to investigate the momentum transfer dependences of the fragment-ion yields and shape resonance features. It is found that the $4{t}_{1u}\ensuremath{\rightarrow}\ensuremath{\varepsilon}{t}_{2g}$ resonance is evident over a wide momentum transfer range, indicating its strong influence on the ${{\mathrm{SF}}_{3}}^{+}$ production by electron impact, while resonance bands in the ${{\mathrm{SF}}_{5}}^{+}$ and ${{\mathrm{SF}}_{4}}^{+}$ yield spectra rapidly diminish with increasing momentum transfer. In addition, the angular distribution of ${{\mathrm{SF}}_{5}}^{+}$ reveals the significant difference in stereodynamics between electron-impact-induced and photon-induced ionization of ${\mathrm{SF}}_{6}$. We also discuss the dissociation mechanisms of ${{\mathrm{SF}}_{6}}^{+}$ using the kinetic energy distributions of the fragment ions. Analysis of the data strongly suggests that many of the ${{\mathrm{SF}}_{6}}^{+}$ ions in the $D\phantom{\rule{0.16em}{0ex}}^{2}T_{2\mathrm{g}}$ state decay by internal conversion to a lower electronic state and dissociate to ${{\mathrm{SF}}_{5}}^{+}+\mathrm{F}$, followed by statistical emission of F or ${\mathrm{F}}_{2}$.