We show that the recent measurements of B_s−B̅_s mass difference, Δm_s, by DØ and CDF collaborations give very strong constraints on MSSM scenario with large flavor mixing in the LL and/or RR sector of down-type squark mass squared matrix. In particular, the region with large mixing angle and large mass difference between scalar strange and scalar bottom is ruled out by giving too large Δm_s. The allowed region is sensitive to the CP violating phases δ_L(R). The Δm_s constraint is most stringent on the scenario with both LL and RR mixing. We also predict the time-dependent CP asymmetry in B_sψφ decay and semileptonic asymmetry in B_sℓX decay.