Metamorphic growth of lattice mismatched InGaP on GaAs has been used to fabricate a fast semiconductor saturable absorber mirror operating at the 1060 nm wavelength range. The absorption recovery time could be reduced to 5 ps without deteriorating the nonlinear absorption properties. The device was used to demonstrate self-starting operation of a mode-locked Yb-doped fiber laser and obtain high quality picosecond pulses