We report on sub-50 fs pulse generation from a passively mode-locked (ML) Tm,Ho-codoped crystalline laser operating in a 2 µm spectral region. A ${\rm Tm},{\rm Ho}{:}{\rm Ca}({\rm Gd},{\rm Lu}){{\rm AlO}_4}$ laser delivers pulses as short as 46 fs at 2033 nm with an average power of 121 mW at a pulse repetition rate of ${\sim}{78}\;{\rm MHz}$ employing a semiconductor saturable absorber mirror as a saturable absorber. To the best of our knowledge, this result represents the shortest pulses ever generated from a Tm- and/or Ho-based solid-state laser. Polarization switching in the anisotropic gain material is observed in the ML regime without any polarization selection elements which is essential for the shortest pulses.