We report on the investigation of continuous-wave (CW) and SEmiconductor Saturable Absorber Mirror (SESAM) mode-locked operation of a Yb:GdScO3 laser. Using a single-transverse-mode, fiber-coupled InGaAs laser diode at 976 nm as a pump source, the Yb:GdScO3 laser delivers 343 mW output power at 1062 nm in the CW regime, which corresponds to a slope efficiency of 52%. Continuous tuning is possible across a wavelength range of 84 nm (1027-1111 nm). Using a commercial SESAM to initiate mode-locking and stabilize soliton-type pulse shaping, the Yb:GdScO3 laser produces pulses as short as 42 fs at 1065.9 nm, with an average output power of 40 mW at 66.89 MHz. To the best of our knowledge, this is the first demonstration of passively mode-locking with Yb:GdScO3 crystal.