A single-crystal of ytterbium-doped “mixed” yttrium-lutetium aluminium garnet with a stoichiometric composition of (Y0.601Lu0.233Yb0.166)3Al5O12 was grown by the Czochralski method and its structure, vibronic, spectroscopic and laser properties were studied. The stimulated-emission cross-section for Yb3+ ions was maximized to 2.53×10-20 cm2 at 1031 nm, the emission bandwidth is ~8 nm and the reabsorption-free luminescence lifetime of the 2F5/2 state is 1.063 ms. Pumped at 941 nm, the Yb-laser generated a maximum output power of 1.04 W at 1.03 and 1.05 μm with a high slope efficiency of 76.4% and a laser threshold of 76 mW. A continuous wavelength tuning over a range of 51.6 nm (1026.4 - 1078.0 nm) was also achieved. Power scaling is achieved using a 969 nm-diode pumped microchip cavity. A maximum output power of ~9 W is obtained at 1.05 μm with a slope efficiency of 76% and with an almost circular laser beam profile.