We have compared stacked spectra of galaxies, grouped by environment and stellar mass, among 58 members of the redshift z = 1.24 galaxy cluster RDCS J1252.9-2927 (J1252.9) and 134 galaxies in the z = 0.84 cluster RX J0152.7-1357 (J0152.7). These two clusters are excellent laboratories to study how galaxies evolve from star-forming to passive at z similar to 1. We measured spectral indices and star-forming fractions for our density- and mass-based stacked spectra. The star-forming fraction among low-mass galaxies (<7 x 10(10) M-circle dot) is higher in J1252.9 than in J0152.7, at about 4 sigma significance. Thus star formation is being quenched between z = 1.24 and z = 0.84 for a substantial fraction of low-mass galaxies. Star-forming fractions were also found to be higher in J1252.9 in all environments, including the core. Passive galaxies in J1252.9 have systematically lower D(n)4000 values than in J0152.7 in all density and mass groups, consistent with passive evolution at modestly super-solar metallicities.