Is it Pope Saint, or Saint Pope?
I’d cast a vote for neither of these clumsy expressions. In the Church’s liturgy, the pope title is nowhere to be seen in litanies of saints. In contrast, conservative Catholic media consistently uses both, often with the abbreviation “Pope St.”.
Vatican document footnotes, something with which I have a fair familiarity, just give the regnal name–current, recent, sainted.
Maybe it depends on the context. A propaganda organ for a pope saint might add “the great” into the mix.
Liturgy is pretty clear: neither for the living, dead, or sainted.
If one is citing papal teaching, then “Pope” seems okay. If one is attending to a matter of spirituality, then “Saint” alone seems the best fit.
Catholic Sensibility 
The English-language title-order convention, at least for Second Millennium popes, has been Pope-Saint for as long as I can remember. That said, a more Roman approach might follow a Latin convention (if there is such a thing) of “Sancti Ioannis XXIII, Papae” = “Saint John XXIII, Pope”.