We report on the first laser operation of a disordered Tm:CaGdAlO4 crystal on the 3H4 → 3H5 transition. Under direct pumping at 0.79 µm, it generates 264 mW at 2.32 µm with a slope efficiency of 13.9% and 22.5% vs. incident and absorbed pump power, respectively, and a linear polarization (σ). Two strategies to overcome the bottleneck effect of the metastable 3F4 Tm3+ state leading to the ground-state bleaching are exploited: cascade lasing on the 3H4 → 3H5 and 3F4 → 3H6 transitions and dual-wavelength pumping at 0.79 and 1.05 µm combining the direct and upconversion pumping schemes. The cascade Tm-laser generates a maximum output power of 585 mW at 1.77 µm (3F4 → 3H6) and 2.32 µm (3H4 → 3H5) with a higher slope efficiency of 28.3% and a lower laser threshold of 1.43 W, out of which 332 mW are achieved at 2.32 µm. Under dual-wavelength pumping, further power scaling to 357 mW at at 2.32 µm is observed at the expense of increased laser threshold. To support the upconversion pumping experiment, excited-state absorption spectra of Tm3+ ions for the 3F4 → 3F2,3 and 3F4 → 3H4 transitions are measured for polarized light. Tm3+ ions in CaGdAlO4 exhibit broadband emission at 2.3 - 2.5 µm making this crystal promising for ultrashort pulse generation.