Using the multi-integral field spectrograph GIRAFFE at VLT, we have derived the K-band Tully-Fisher relation (TFR) at z sim 0.6 for a representative sample of 65 galaxies with emission lines (W_\mathrm{0}\mathrm\ge15 similar to \AA). We confirm that the scatter in the z sim 0.6 TFR is caused by galaxies with anomalous kinematics, and find a positive and strong correlation between the complexity of the kinematics and the scatter that they contribute to the TFR. Considering only relaxed-rotating disks, the scatter, and possibly also the slope, of the TFR, do not appear to evolve with redshift. We detect an evolution of the K-band TFR zero point between z sim 0.6 and z =0, which, if interpreted as an evolution of the K-band luminosity of rotating disks, would imply that a brightening of 0.66 pm 0.14 mag occurs between z sim 0.6 and z =0. Any disagreement with the results of Flores et al. (2006, A&A, 455, 107) are attributed to both an improvement of the local TFR and the more detailed accurate measurement of the rotation velocities in the distant sample. Most of the uncertainty can be explained by the relatively coarse spatial-resolution of the kinematical data. Because most rotating disks at z sim 0.6 are unlikely to experience further merging events, one may assume that their rotational velocity, which is taken as a proxy of the total mass, does not evolve dramatically. If true, our result implies that rotating disks observed at z sim 0.6 are rapidly transforming their gas into stars, to be able to double their stellar masses and be observed on the TFR at z =0. The rotating disks observed are indeed emission-line galaxies that are either starbursts or LIRGs, which implies that they are forming stars at a high rate. Thus, a significant fraction of the rotating disks are forming the bulk of their stars within 6 to 8 Gyr, in good agreement with former studies of the evolution of the mass-metallicity relationship.