A high-power sub-60 fs mode-locked diode-pumped Yb:KGW laser based on hybrid action of an InGaAs quantum-dot saturable absorber mirror and Kerr-lens mode locking was demonstrated. The laser delivered 56 fs pulses with 1.95 W of average power corresponding to 450 kW of peak power. The width of the generated laser spectrum was 20.5 nm, which was near the gain bandwidth limit of the Yb:KGW crystal. To the best of our knowledge, these are the shortest pulses generated from the monoclinic double tungstate crystals (and Yb:KGW laser crystal in particular) and the most powerful in the sub-60 fs regime. At the same time, they are also the shortest pulses produced to date with the help of a quantum-dot-based saturable absorber. High-power operation with a pulse duration of 90 fs and 2.85 W of average output power was also demonstrated.