We developed a new digital etch process that allows precise etching of Germanium or Germanium-tin (Ge1-x Sn x ) materials. The digital etch approach consists of Ge1-x Sn x oxide formation by plasma oxidation and oxide removal in diluted hydrochloric acid at room temperature. The first step is a self-limiting process, as the thickness of oxide layer grows logarithmically with the oxidation time and saturates fast. Consistent etch rates in each cycle were found on the Ge1-x Sn x samples, with the surfaces remaining smooth after etch. The digital etch process parameters were tuned to achieve various etch rates. By reducing the radio frequency power to 70 W, etch rate of sub-1.2 nm was obtained on a Ge0.875Sn0.125 sample. The digital etch process was employed to fabricate the Ge1-x Sn x fin structures. Extremely scaled Ge0.95Sn0.05 fins with 5 nm fin width were realized. The side walls of the Ge0.95Sn0.05 fins are smooth, and no crystal damage can be observed. This technique provides an option to realize aggressively scaled nanostructure devices based on Ge1-x Sn x materials with high-precision control.