Mize (4-7) allowed eight runs on nine hits and three walks while striking out one over 3.1 innings to take the loss versus the Diamondbacks on Wednesday.
Tatis went 1-for-4 with a solo home run in Wednesday's 10-4 loss to the Diamondbacks.
General manager Ben Cherington said that there is no timeline for Cruz (hand) to return from the injured list, Colin Beazley of the Pittsburgh Post-Gazette reports.
Skenes (9-10) allowed three runs on two hits and four walks while striking out six over five innings to take the loss versus the Brewers on Wednesday.
Rodriguez went 1-for-3 with a two-run home run in Wednesday's 4-2 loss to the Brewers.
Mize will start Wednesday's game against the Diamondbacks in Arizona.
The Pirates selected Simon's contract from Triple-A Indianapolis on Wednesday.
Pittsburgh reinstated Sisk (elbow) from the 15-day injured list Wednesday.
Bogaerts (foot) is starting at shortstop and batting sixth against the Diamondbacks on Wednesday, AJ Cassavell of MLB.com reports.
Horwitz is not in the Pirates' starting lineup against the Brewers on Wednesday.
