Most magnetic refrigeration materials showing a large and reversible magnetocaloric effect (MCE) undergo a second-order ferromagnetic (FM) transition involving large-moment magnetic species on one sublattice. A stronger MCE is expected near a cooperative FM order of two or more magnetic species with large magnetic moments residing on different sublattices, but experimental realizations are rare. Here we report on the discovery of large MCE in the cubic pyrochlore $\mathrm{E}{\mathrm{r}}_{2}\mathrm{M}{\mathrm{n}}_{2}{\mathrm{O}}_{7}$ near its second-order FM transition at ${T}_{c}\ensuremath{\approx}34\phantom{\rule{0.16em}{0ex}}\mathrm{K}$; under the magnetic field change of 1 and 5 T, the maximum magnetic entropy change $\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{M}$ is 5.27 and $16.1\phantom{\rule{0.16em}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{k}{\mathrm{g}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$, and the estimated magnetic refrigerant capacity reaches 68 and $522\mathrm{J}\phantom{\rule{0.16em}{0ex}}\mathrm{k}{\mathrm{g}}^{\ensuremath{-}1}$, respectively. These latter values are among the largest for the known MCE materials. The observed giant and reversible MCE in $\mathrm{E}{\mathrm{r}}_{2}\mathrm{M}{\mathrm{n}}_{2}{\mathrm{O}}_{7}$ is mainly attributed to the large saturation moment of $18.9\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$ per formula unit owing to a simultaneous FM ordering of the rear-earth ${\mathrm{Er}}^{3+}$ and transition-metal ${\mathrm{Mn}}^{4+}$ localized moments. Our results suggest that $\mathrm{E}{\mathrm{r}}_{2}\mathrm{M}{\mathrm{n}}_{2}{\mathrm{O}}_{7}$ pyrochlore is a promising candidate for magnetic refrigeration applications in the temperature range 20--80 K. More importantly, this work provides a new material system for developing high-performance MCE materials that can exhibit a strongly coupled FM transition involving two magnetic sublattices of large local moments in a single-phase material.