We present a detailed continuous-wave regime characterization and, for the first time to the best of our knowledge, SESAM mode-locked femtosecond operation with a monoclinic, Yb3+-doped, MgWO4 crystal. Pumping with a low-power, single-mode fiber-coupled laser diode emitting at 976 nm, we demonstrate threshold for continuous-wave (cw) operation as low as 50 mW (absorbed pump power) and slope efficiency up to ~60% (with respect to the absorbed pump power) for two of the principal emission polarizations. The output wavelength in the cw regime is continuously tunable over a ∼50 nm broad range. Mode-locking the laser with a SESAM, we achieve almost Fourier-transform limited pulses with a duration of 132 and 125 fs depending on the polarization.