We compare the star formation ( SF ) activity in cluster galaxies to the field from z = 0.3 - 1.5 using Herschel Spectral and Photometric Imaging REceiver ( SPIRE ) 250 \mu m imaging . We utilize 274 clusters from the IRAC Shallow Cluster Survey ( ISCS ) selected as rest-frame near-infrared overdensities over the 9 square degree Boötes field . This analysis allows us to quantify the evolution of SF in clusters over a long redshift baseline without bias against active cluster systems . Using a stacking analysis , we determine the average star formation rates ( SFRs ) and specific-SFRs ( SSFR=SFR/M _ { \star } ) of stellar mass-limited ( M \geq 1.3 \times 10 ^ { 10 } \mathrm { M _ { \odot } } ) , statistical samples of cluster and field galaxies , probing both the star forming and quiescent populations . We find a clear indication that the average SF in cluster galaxies is evolving more rapidly than in the field , with field SF levels at z { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 1.2 in the cluster cores ( r < 0.5 Mpc ) , in good agreement with previous ISCS studies . By quantifying the SF in cluster and field galaxies as an exponential function of cosmic time , we determine that cluster galaxies are evolving \sim 2 times faster than the field . Additionally , we see enhanced SF above the field level at z \sim 1.4 in the cluster outskirts ( r > 0.5 Mpc ) . These general trends in the cluster cores and outskirts are driven by the lower mass galaxies in our sample . Blue cluster galaxies have systematically lower SSFRs than blue field galaxies , but otherwise show no strong differential evolution with respect to the field over our redshift range . This suggests that the cluster environment is both suppressing the star formation in blue galaxies on long time-scales and rapidly transitioning some fraction of blue galaxies to the quiescent galaxy population on short time-scales . We argue that our results are consistent with both strangulation and ram pressure stripping acting in these clusters , with merger activity occurring in the cluster outskirts .