  The presence of massive neutrinos has a characteristic impact on the growth
of large scale structures such as galaxy clusters. We forecast on the
capability of the number count and power spectrum measured from the ongoing and
future Sunyaev-Zeldovich (SZ) cluster surveys, combined with cosmic microwave
background (CMB) observation to constrain the total neutrino mass $\mnu$ in a
flat $\Lambda$CDM cosmology. We adopt self-calibration for the mass-observable
scaling relation, and evaluate constraints for the South Pole Telescope normal
and with polarization (SPT, SPTPol), Planck, and Atacama Cosmology Telescope
Polarization (ACTPol) surveys. We find that a sample of $\approx1000$ clusters
obtained from the Planck cluster survey plus extra information from CMB lensing
extraction could tighten the current upper bound on the sum of neutrino masses
to $\sigma_{\mnu}=0.17$ eV at 68% C.L. Our analysis shows that cluster number
counts and power spectrum provide complementary constraints and as a result
they help reducing the error bars on $\mnu$ by a factor of 4-8 when both probes
are combined. We also show that the main strength of cluster measurements in
constraining $\mnu$ is when good control of cluster systematics is available.
When applying a weak prior on the mass-observable relations, which can be at
reach in the upcoming cluster surveys, we obtain $\sigma_{\mnu}=0.48$ eV using
cluster only probes and, more interestingly, $\sigma_{\mnu}=0.08$ eV using
cluster + CMB which corresponds to a $S/N\approx4$ detection for $\mnu\ge0.3$
eV. We analyze and discuss the degeneracies of $\mnu$ with other parameters and
investigate the sensitivity of neutrino mass constraints with various surveys
specifications.
