A grating waveguide mirror (GWM) results from the combination of a waveguide and a sub-wavelength grating which lead, for given incidence conditions, to polarization and or wavelength filtering. In the present paper, we report on the application of such elements for the selection of the polarization (linear, radial, or azimuthal) as well as the narrowing, stabilizing and tuning of the emission spectrum of high-power lasers. Using a leaky-mode circular GWM, beams with radial and azimuthal polarization with output powers of up to 275 W and 145 W, respectively, could be extracted from a Yb:YAG thin-disk with optical efficiencies of 52.5% and 43%, respectively. In both cases, the GWM was composed of a highly reflective (HR) mirror and a sub-wavelength grating as the end-mirror of the resonator. Using a leaky-mode linear GWM operating under Littrow condition, beams with linear polarization and a narrow spectral bandwidth were obtained from a Yb:YAG thin-disk laser. In multimode operation, an output power of 325 W was achieved at an optical efficiency of 53.5%. In near-fundamental mode operation, 110 W was extracted at an optical efficiency of 36.2%. In this latter case, the spectral bandwidth was measured to be around 25 pm. Moreover, continuous wavelength tuning from 1007 to 1053 nm was demonstrated with our device.