The X-ray free-electron laser has opened a new era for photon science, improving the X-ray brightness by ten orders of magnitude over previously available sources. Similar to an optical laser, the spectral and temporal structure of the radiation pulses can be tailored to the specific needs of many experiments by accurately manipulating the lasing medium, that is, the electron beam. Here we report the generation of mJ-level two-colour hard X-ray pulses of few femtoseconds duration with an XFEL driven by twin electron bunches at the Linac Coherent Light Source. This performance represents an improvement of over an order of magnitude in peak power over state-of-the-art two-colour XFELs. The unprecedented intensity and temporal coherence of this new two-colour X-ray free-electron laser enable an entirely new set of scientific applications, ranging from X-ray pump/X-ray probe experiments to the imaging of complex biological samples with multiple wavelength anomalous dispersion.