We report distinct laser performance of Yb:Gd ${\mathrm{Ca}}_4\mathrm{O}({\mathrm{BO}}_3{)}_3$ crystals cut along different principal optical axes using an unpolarized diode pump. The continuous-wave (cw) laser oscillation generated with y-cut crystal is polarized either with $\mathbf{E}\parallel x$ or with $\mathbf{E}\parallel z$ depending on the output coupling (T) utilized; a specific $T=3\%$ leads to a special situation in which the two orthogonal polarization states coexist oscillating at different wavelengths. The laser oscillation achieved with x- and z-cut crystals is also polarized, but with a fixed polarization of $\mathbf{E}\parallel z$ and $\mathbf{E}\parallel x$ , respectively. The most efficient laser operation is obtained with the y-cut crystal, generating a cw output power of $7.35\mathrm{W}$ at $1083–1085\mathrm{nm}$ with an optical-to-optical efficiency of 63%, the slope efficiency being as high as 84%.