Use of a V(3+):Y(3)Al(5)O(12) crystal as a saturable absorber Q-switch for 1.07 and 1.35 microm Nd:KGd(WO(4))(2) diode pumped lasers shows a considerable dependence of output characteristics on the orientation of the intracavity field polarization vector regarding V(3+):Y(3)Al(5)O(12) crystallographic axes. Anisotropy of nonlinear absorption of V(3+) ions in a Y(3)Al(5)O(12) single crystal at wavelengths of 1.08 and 1.35 microm has been experimentally studied. The experimental data are analyzed within the framework of a phenomenological model when the V(3+) ions are described as three sets of linear dipoles oriented along the crystallographic axes. Ground-state and excited-state absorption cross sections at 1.08 and 1.35 mum are evaluated to be sigma(gsa)=3.4x10(-18) cm(2), sigma(esa)=3.0x10(-19) cm(2) and sigma(gsa)=5.4x10(-18) cm(2), sigma(esa)=4.8x10(-19) cm(2), respectively. Saturation fluence and intensity at 1.08 and 1.35 microm are estimated as 55 mJ/cm(2) and 1.1 MW/cm(2), respectively.