The SASE3 soft X-ray beamline at the European XFEL has been designed and built to provide experiments with pink or monochromatic beam in the photon energy range 250 eV - 3000 eV. Here, we focus on the monochromatic operation of the SASE3 beamline and report on design and performance of the SASE3 grating monochromator. The unique capability of an FEL source to produce short femtosecond pulses of high degree of coherence challenges the monochromator design by a demand to control both photon energy and temporal resolution. The aim to transport close to transform-limited pulses poses very high demands on the optics quality, in particular on the grating. The current realization of the SASE3 monochromator is discussed in comparison with optimal design performance. Presently, the monochromator operates with two gratings: the low-resolution grating is optimized for time-resolved experiments and allows for moderate resolving power of about 2000 - 5000 along with pulse stretching of few to few tens of femtoseconds RMS, and the high-resolution grating reaches resolving power of 10000 at a cost of larger pulse stretching.