Most stars in galactic discs are believed to be born as a member of star clusters or associations. Star clusters formed in discs are disrupted due to the tidal stripping and the evolution of star clusters themselves, and as a result new stars are supplied to the galactic discs. We performed N-body simulations of star clusters in galactic discs, in which both star clusters and galactic discs are modelled as N-body (‘live’) systems, and as a consequence the discs form transient and recurrent spiral arms. In such non-steady spiral arms, star clusters migrate radially due to the interaction with spiral arms. We found that the migration time-scale is a few hundred Myr and that the angular momentum changes of star clusters are at most ∼50 per cent in 1 Gyr. Radial migration of star clusters to the inner region of galaxies results in a fast disruption of the star clusters because of a stronger tidal field in the inner region of the galaxy. This effect is not negligible for the disruption time-scale of star clusters in galactic discs. Stars stripped from clusters form tidal tails which spread over 1–2 kpc. While the spatial distribution of tidal tails changes in a complicated way due to the non-steady spiral arms, the velocity distribution conserves well even if the tidal tails are located at a few kpc from their parent clusters. Tidal tails of clusters in galactic discs might be detected using velocity plots.