We report the spectroscopy and high-power continuous-wave (CW) diode-pumped laser operation of $\mathrm{Er}:\mathrm{Yb}:{\mathrm{YAl}}_3({\mathrm{BO}}_3{)}_4$ crystal. Absorption and stimulated emission spectra, emission lifetimes, and efficiency of energy transfer from ${\mathrm{Yb}}^{3+}$ to ${\mathrm{Er}}^{3+}$ ions were determined. A CW $\mathrm{Er}:\mathrm{Yb}:\mathrm{YAB}$ laser emitting at 1602, 1555, and $1531\mathrm{nm}$ with output power as high as $1\mathrm{W}$ and slope efficiency up to 35% was demonstrated.