The iron-chalcogenide superconductor FeTe1–xSex displays a variety of exotic features distinct from iron pnictides. Although much effort has been devoted to understanding the interplay between magnetism and superconductivity near x = 0.5, the existence of a spin glass phase with short-range magnetic order in the doping range (x ∼ 0.1–0.3) has rarely been studied. Here, we use DC/AC magnetization and (quasi) elastic neutron scattering to confirm the spin-glass nature of the short-range magnetic order in a Fe1.07Te0.8Se0.2 sample. The AC-frequency dependent spin-freezing temperature Tf generates a frequency sensitivity ΔTf(ω)/[Tf(ω)Δlog10 ω] ≈ 0.028 and the description of the critical slowing down with τ = τ0(Tf/TSG – 1)−z v gives TSG ≈ 22 K and zv ≈ 10, comparable to that of a classical spin-glass system. We have also extended the frequency-dependent Tf to the smaller time scale using energy-resolution-dependent neutron diffraction measurements, in which the TN of the short-range magnetic order increases systematically with increasing energy resolution. By removing the excess iron through annealing in oxygen, the spin-freezing behavior disappears, and bulk superconductivity is realized. Thus, the excess Fe is the driving force for the formation of the spin-glass phase detrimental to bulk superconductivity.