Miss. Code § 99-39-29
If the prisoner or prisoners shall be under sentence of death and the date fixed for the execution of the sentence shall arrive at a time when proceedings for post-conviction collateral relief are pending, either in the state or the federal courts, the Supreme Court of Mississippi shall have the authority to stay the execution upon a substantial showing of merit pending the determination of said proceeding. If, however, a stay has been entered either by a state or federal court and post-conviction collateral relief is denied, the Supreme Court of Mississippi shall forthwith fix a day, not more than thirty (30) days distant from the date of said denial or the vacating of any stay entered by any federal court, for the execution of the sentence, and a warrant shall forthwith issue accordingly.
Miss. Code § 99-39-29