We present a velocity dispersion-based mass calibration of the South Pole Telescope Sunyaev-Zel ’ dovich effect survey ( SPT-SZ ) galaxy cluster sample . Using a homogeneously selected sample of 100 cluster candidates from 720 deg ^ { 2 } of the survey along with 63 velocity dispersion ( \sigma _ { v } ) and 16 X-ray Y _ { \textrm { X } } measurements of sample clusters , we simultaneously calibrate the mass-observable relation and constrain cosmological parameters . Our method accounts for cluster selection , cosmological sensitivity , and uncertainties in the mass calibrators . The calibrations using \sigma _ { v } and Y _ { \textrm { X } } are consistent at the 0.6 \sigma level , with the \sigma _ { v } calibration preferring \sim 16 % higher masses . We use the full SPT _ { \textrm { CL } } dataset ( SZ clusters+ \sigma _ { v } + Y _ { \textrm { X } } ) to measure \sigma _ { 8 } ( \Omega _ { \textrm { m } } / 0.27 ) ^ { 0.3 } = 0.809 \pm 0.036 within a flat \Lambda CDM model . The SPT cluster abundance is lower than preferred by either the WMAP9 or Planck +WMAP9 polarization ( WP ) data , but assuming the sum of the neutrino masses is \sum m _ { \nu } = 0.06 eV , we find the datasets to be consistent at the 1.0 \sigma level for WMAP9 and 1.5 \sigma for Planck +WP . Allowing for larger \sum m _ { \nu } further reconciles the results . When we combine the SPT _ { \textrm { CL } } and Planck +WP datasets with information from baryon acoustic oscillations and supernovae Ia , the preferred cluster masses are 1.9 \sigma higher than the Y _ { \textrm { X } } calibration and 0.8 \sigma higher than the \sigma _ { v } calibration . Given the scale of these shifts ( \sim 44 % and \sim 23 % in mass , respectively ) , we execute a goodness of fit test ; it reveals no tension , indicating that the best-fit model provides an adequate description of the data . Using the multi-probe dataset , we measure \Omega _ { \textrm { m } } = 0.299 \pm 0.009 and \sigma _ { 8 } = 0.829 \pm 0.011 . Within a \nu CDM model we find \sum m _ { \nu } = 0.148 \pm 0.081 eV . We present a consistency test of the cosmic growth rate using SPT clusters . Allowing both the growth index \gamma and the dark energy equation of state parameter w to vary , we find \gamma = 0.73 \pm 0.28 and w = -1.007 \pm 0.065 , demonstrating that the expansion and the growth histories are consistent with a \Lambda CDM Universe ( \gamma = 0.55 ; w = -1 ) .