We present an analysis of the MgII 2796, 2803 and FeII 2586, 2600 absorption line profiles in coadded spectra of 468 galaxies at 0.7 < z < 1.5. The galaxy sample, drawn from the Team Keck Treasury Redshift Survey of the GOODS-N field, has a range in stellar mass (M_*) comparable to that of the sample at z~1.4 analyzed in a similar manner by Weiner et al. (2009; W09), but extends to lower redshifts and has specific star formation rates which are lower by ~0.6 dex. We identify outflows of cool gas from the Doppler shift of the MgII absorption lines and find that the equivalent width (EW) of absorption due to outflowing gas increases on average with M_* and star formation rate (SFR). We attribute the large EWs measured in spectra of the more massive, higher-SFR galaxies to optically thick absorbing clouds having large velocity widths. The outflows have hydrogen column densities N(H) > 10^19.3 cm^-2, and extend to velocities of ~500 km/s. While galaxies with SFR > 10 Msun/yr host strong outflows in both this and the W09 sample, we do not detect outflows in lower-SFR (i.e., log M_*/Msun < 10.5) galaxies at lower redshifts. Using a simple galaxy evolution model which assumes exponentially declining SFRs, we infer that strong outflows persist in galaxies with log M_*/Msun > 10.5 as they age between z=1.4 and z~1, presumably because of their high absolute SFRs. Finally, using high resolution HST/ACS imaging in tandem with our spectral analysis, we find evidence for a weak trend (at 1 sigma significance) of increasing outflow absorption strength with increasing galaxy SFR surface density.