We observed plastic deformation of diamond by mechanical twinning at temperatures substantially below the Debye temperature. Twinning occurred during the processing in a planetary mill of nano-diamond with an average grain size of 10 nm mixed with silicon. Under the experimental conditions, the maximum stresses in diamond are limited by the hardness of steel balls (7 GPa), which is much lower than the critical shear stresses for diamond (55 GPa), when plastic deformation of diamond is observed under static loads and temperatures below Debye temperature.