We report on a high-power diode-pumped Yb:KG(WO4)2 (Yb:KGW) mode-locked laser with a semiconductor saturable absorber mirror (SESAM). For 32.7 W of incident pump power, we generate 261 fs pulses with the maximum average output power of up to 13.0 W and spectrum centered around 1039 nm at 68.4 MHz, corresponding to 190 nJ of single pulse energy and 0.72 MW of peak power. The optical-to-optical conversion efficiency is 39.8%, and the slope efficiency is 64.4%. The Yb:KGW laser exhibits a power stability better than 0.543% of the root-mean-square in 2 h.