Tetragonal calcium rare-earth aluminates, CaLnAlO4, combine a structural disorder with good thermo-mechanical properties. We report on efficient continuous-wave (CW) and passively Q-switched (PQS) ∼2-μm laser operation of a 4 at.% Tm:CaYAlO4 crystal using a compact (6-mm-long) plane-parallel cavity. The pump source was a 791 nm fibercoupled AlGaAs laser diode. The CW output power reached 5.78 W at ∼1970 nm with a slope efficiency of 43.6% and a linear laser polarization. Stable PQS operation was achieved using a single-walled carbon nanotube (SWCNT) based transmission-type saturable absorber. The PQS laser generated 2.15 W at ∼1945 nm, a record-high average output power for this type of lasers. The best pulse characteristics (energy/duration) were 9.1 μJ/165 ns at a repetition rate of 235 kHz.