  We derive new model independent constraints on the supersymmetric extensions
of the standard model from the new experimental measurements of B_s -\bar{B}_s
mass difference. We point out that supersymmetry can still give a significant
contribution to the CP asymmetry of B_s ->J/\psi \phi that can be measured at
the LHCb experiment. These new constraints on the LL and RR squark mixing
severely restricted their possible contributions to the CP asymmetries of B->
\phi K and B - >\eta' K. Therefore, SUSY models with dominant LR flavor mixing
is the only way to accommodate the apparent deviation of CP asymmetries from
those expected in the standard model. Finally we present an example of SUSY
non-minimal flavor model that can accommodate the new \Delta M_{B_s} results
and also induces significant CP asymmetries in B_s ->J/\psi \phi, B->\phi K and
B ->\eta' K processes.
