We demonstrate the first realization of electron beam and x-ray pulse shaping with a corrugated wakefield structure at a pulsed-mode megahertz repetition rate hard x-ray free-electron laser. This is achieved by an L-shape-designed corrugated structure with low beta optics and a collimator. Variable streaking direction and signature of quadrupole wakefield compensation are observed by controlling the position of the electron beam to the corrugated plates. Spectral analysis at 7 keV indicates a reduction of the reconstructed x-ray pulse duration by an approximate factor of four compared to the standard self-amplified spontaneous emission mode of the European X-ray Free-electron Laser. X-ray pulses with uniform properties along a train of 100 pulses at 1.125 MHz repetition rate are generated under 10 Hz pulse mode. These results are a step toward tailoring the temporal and spectral domain of x-ray pulses at megahertz repetition rate with high flexibility and compatibility.