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We present the Stage II results from the ongoing Satellites Around Galactic Analogs (SAGA) Survey. Upon completion, the SAGA Survey will spectroscopically identify satellite galaxies brighter than $ M_{r,o} = -12.3 $ around 100 Milky Way (MW) analogs at $ z \sim 0.01 $. In Stage II, we have more than quadrupled the sample size of Stage I, delivering results from 127 satellites around 36 MW analogs with an improved target selection strategy and deep photometric imaging catalogs from the Dark Energy Survey and the Legacy Surveys. We have obtained 25,372 galaxy redshifts, peaking around $ z = 0.2 $. These data significantly increase spectroscopic coverage for very low redshift objects in $ 17 < r_o < 20.75 $ around SAGA hosts, creating a unique data set that places the Local Group in a wider context. The number of confirmed satellites per system ranges from zero to nine, and correlates with host galaxy and brightest satellite luminosities. We find that the number and the luminosities of MW satellites are consistent with being drawn from the same underlying distribution as SAGA systems. The majority of confirmed SAGA satellites are star forming, and the quenched fraction increases as satellite stellar mass and projected radius from the host galaxy decrease. Overall, the satellite quenched fraction among SAGA systems is lower than that in the Local Group. We compare the luminosity functions and radial distributions of SAGA satellites with theoretical predictions based on cold dark matter simulations and an empirical galaxy-halo connection model and find that the results are broadly in agreement.