In frustrated magnetic systems, geometric constraints or the competition among interactions introduce extremely high degeneracy and prevent the system from readily selecting a low-temperature ground state. The most frustrated known spin arrangement is on the pyrochlore lattice, but nearly all magnetic pyrochlores have unquenched orbital angular momenta, constraining the spin directions through spin-orbit coupling. Pyrochlore Mn₂Sb₂O₇ is an extremely rare Heisenberg pyrochlore system with directionally unconstrained spins and low chemical disorder. We show that it undergoes a spin-glass transition at 5.5 K, which is suppressed by disorder arising from Mn vacancies, indicating this ground state to be a direct consequence of the spins' interactions. The striking similarities to 3d transition-metal pyrochlores with unquenched angular momenta suggests that the low spin-orbit coupling in the 3d block makes Heisenberg pyrochlores far more accessible than previously imagined.