We present a study of the H II regions in the galaxy NGC 6754 from a two pointing mosaic comprising 197 637 individual spectra, using integral field spectroscopy recently acquired with the MUSE instrument during its Science Verification program. The data cover the entire galaxy out to ~2 effective radii (re), sampling its morphological structures with unprecedented spatial resolution for a wide-field Integral Field Unit. A complete census of the H II regions limited by the atmospheric seeing conditions was derived, comprising 396 individual ionized sources. This is one of the largest and most complete catalogues of H II regions with spectroscopic information in a single galaxy. We use this catalogue to derive the radial abundance gradient in this SBb galaxy, finding a negative gradient with a slope consistent with the characteristic value for disk galaxies recently reported. The large number of H II regions allows us to estimate the typical mixing scale length (rmix ~ 0.4re), which sets strong constraints on the proposed mechanisms for metal mixing in disk galaxies, like radial movements associated with bars and spiral arms. We found evidence of an azimuthal variation in the oxygen abundance that may be connected with the radial migration. These results illustrate the unique capabilities of MUSE for the study of the enrichment mechanisms in Local Universe galaxies.