It all depends on Pettitte's elbow. Considering the state of the bullpen (Robertson's ineffectiveness and Park's injury), I think they'd be very reluctant to put Aceves into the starting rotation. So, on the MLB team right now, all they have is Mitre.
As for guys coming up from the minors, to the best of my knowledge, they're pretty thin when it comes to high level pitching. The best options would probably be someone like Hirsch or Mosley.
With Pettitte's start almost certainly being pushed back, they're probably going to slot Mitre into Tuesday's start, and unless Pettitte's injury is serious, Mitre will probably start in his place until Pettitte is good to go.
Once Pettitte is healthy, if Vazquez can't go, I'd suspect Mitre would then take his place. However, if both Pettitte and Vazquez can't go, I'd imagine they'd be tempted to go outside the organization for help.