We present results on the clustering properties of galaxies as a function of both stellar mass and specific star formation rate (sSFR) using data from the PRIMUS and DEEP2 galaxy redshift surveys spanning 0.2 < z < 1.2. We use spectroscopic redshifts of over 100,000 galaxies covering an area of 7.2 deg^2 over five separate fields on the sky, from which we calculate cosmic variance errors. We find that the galaxy clustering amplitude is as strong of a function of sSFR as of stellar mass, and that at a given sSFR, it does not significantly depend on stellar mass within the range probed here. We further find that within the star-forming population and at a given stellar mass, galaxies above the main sequence of star formation with higher sSFR are less clustered than galaxies below the main sequence with lower sSFR. We also find that within the quiescent population, galaxies with higher sSFR are less clustered than galaxies with lower sSFR, at a given stellar mass. We show that the galaxy clustering amplitude smoothly increases with both increasing stellar mass and decreasing sSFR, implying that galaxies likely evolve across the main sequence, not only along it, before galaxies eventually become quiescent. These results imply that the stellar mass to halo mass relation, which connects galaxies to dark matter halos, likely depends on sSFR.