Assuming no new injuries, here are the players in consideration for the active roster before the end of the season. Currently injured players with best-guess return date. Pitchers: P. López, Gray, Ryan, Ober, Maeda, Keuchel, Thielbar (August 1), Stewart (August 10), Moran, Sands, J. López, Balazovic, Ortega, Pagán, Jax, Duran. Position Players: Vázquez, Jeffers, Kirilloff, Julien, Correa, Farmer, Lewis (August 15), Polanco (August 1), Solano, Gallo, Taylor, Kepler, Castro, Wallner, Larnach, Buxton. By my count that is 16 pitchers for 13 spots and 16 position players for 13 spots.
The three pitchers to cut (IMHO) would be Sands, Ortega and Jorge López, I guess. The three position players to be sent down--Wallner, Larnach and Gallo (DFA)?
I didn't list Nick Gordon, Gilberto Celestino, Jose Miranda, Headrick or Winder. Gordon and Miranda are currently on major league Injured Lists. I would assume the Twins would add Gordon only after September 1, since he can't be optioned. I also assume injuries will take care of some of this roster glut, but this does point out how difficult making a move at the deadline will be. Players the Twins want to keep in Minnesota will be optioned or DFAed unless they trade someone from the 40-man roster.