  We have carried out spectroscopic observations in 4 cluster fields using
Subaru's FOCAS multi-slit spectrograph and obtained spectra for 103 bright disk
field and cluster galaxies at $0.06 \le z \le 1.20$. Seventy-seven of these
show emission lines, and 33 provide reasonably-secure determinations of the
galaxies' rotation velocity. The rotation velocities, luminosities, colours and
emission-line properties of these galaxies are used to study the possible
effects of the cluster environment on the star-formation history of the
galaxies. Comparing the Tully-Fisher relations of cluster and field galaxies at
similar reshifts we find no measurable difference in rest-frame $B$-band
luminosity at a given rotation velocity (the formal difference is $0.18\pm0.33
$mag). The colours of the cluster emission line galaxies are only marginally
redder in rest-frame $B-V$ (by $0.06\pm0.04 $mag) than the field galaxies in
our sample. Taken at face value, these results seem to indicate that bright
star-forming cluster spirals are similar to their field counterparts in their
star-formation properties. However, we find that the fraction of disk galaxies
with absorption-line spectra (i.e., with no current star formation) is larger
in clusters than in the field by a factor of $\sim3$--5. This suggests that the
cluster environment has the overall effect of switching off star formation in
(at least) some spiral galaxies. To interpret these observational results, we
carry out simulations of the possible effects of the cluster environment on the
star-formation history of disk galaxies and thus their photometric and
spectroscopic properties. Finally, we evaluate the evolution of the rest-frame
absolute $B$-band magnitude per unit redshift at fixed rotation velocity.
