We investigate the evolution of the galaxy stellar mass function and stellar mass density from redshift z= 0.2 to z= 1.5 of a K sub(s)< 22-selected sample with highly reliable photometric redshifts and over an unprecedentedly large area. Our study is based on near-infrared observations carried out with the WIRCam instrument at CFHT over the footprint of the VIPERS spectroscopic survey and benefits from the high-quality optical photometry from the CFHTLS and ultraviolet observations with the GALEX satellite. The accuracy of our photometric redshifts is sigma sub(Delta)z/ (1 + z)< 0.03 and 0.05 for the bright (i sub(AB)< 22.5) and faint (i sub(AB)> 22.5) samples, respectively. The galaxy stellar mass function is measured with ~760000 galaxies down to K sub(s)~ 22 and over an effective area of ~22.4 deg super(2), the latter of which drastically reduces the statistical uncertainties (i.e. Poissonian error and cosmic variance). We point out the importance of carefully controlling the photometric calibration, whose effect becomes quickly dominant when statistical uncertainties are reduced, which will be a major issue for future cosmological surveys with EUCLID or LSST, for instance. By exploring the rest-frame (NUV?r) vs. (r?K sub(s)) colour-colour diagram with which we separated star-forming and quiescent galaxies, (1) we find that the density of very massive log(M sub(?)/M sub(?)) > 11.5 galaxies is largely dominated by quiescent galaxies and increases by a factor 2 from z~ 1 to z~ 0.2, which allows for additional mass assembly through dry mergers. (2) We also confirm the scenario in which star formation activity is impeded above a stellar mass log(? super(*) sub(SF)/M sub(?)) = 10.64+ or -0.01. This value is found to be very stable at 0.2 <z< 1.5. (3) We discuss the existence of a main quenching channel that is followed by massive star-forming galaxies, and we finally (4) characterise another quenching mechanism that is required to explain the clear excess of low-mass quiescent galaxies that is observed at low redshift.