A Tm,Ho:CALGO laser passively mode-locked by a GaSb-based SESAM generated pulses as short as 52 fs at a central wavelength of 2015 nm with a broad spectral bandwidth of 82 nm (full width at half maximum) owing to the combined gain profiles of both dopants for σ-polarized light. The average output power reached 376 mW at a repetition rate of 85.65 MHz. In the continuous-wave regime, the laser was power scaled up to 1.01 W at 2080.6 nm with a slope efficiency of 32.0%, a laser threshold of 155 mW and π-polarized emission. Polarized spectroscopic properties of Ho3+ ions in singly doped and codoped CALGO crystals were revisited to explain the observed laser performance.