DE Jason Pierre-Paul is not on the roster at this time because he has not signed his franchise tender. Whether or not he is ready to play, it is likely he will be placed on NFI (non-football injury list) when he signs, therefore missing the first six games of the season.
Decisions still have to be made on CB Chykie Brown (knee), S Nat Berhe (calf) and DB Bennett Jackson (knee). Only one can be placed on short-term IR. I doubt they'd burn that on Brown and Jackson and Berhe are projected to be out for the entire season.
In short, the Giants will have about 8-9 actual cuts to make by Tuesday. - Fennelly