Why would Turbotax show my state return received and the state of Mississippi does not?

TurboTax never shows that your refund was "received".  TurboTax only shows you that your return was "accepted" and gives you an estimated date to receive the refund.  TT never knows if the IRS or state issues your refund; the IRS and/or states do not provide any information to TurboTax after you file your tax return.

Federal and state refunds come from completely separate entities,  There is no rule as to which one will come first or how much time there will be between their arrivals.  Some states process returns quickly and some are very slow.

STATE RETURN

Make sure your state return was accepted:  https://turbotax.intuit.com/tax-tools/efile-status-lookup/

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573