It's important to note the difference between verbal irony and sarcasm (which is always verbal). The primary difference is that sarcasm is wilfully intended to injure the person being addressed. Irony may be neutral, without intent to hurt, only pointing out the amusing difference between an expectation and the reality. Sarcasm, though, is always intended as an injury to another person's feelings.

With this clarification, I don't find extensive instances of sarcasm. Both Jig and the American are sincere in their expressions and feelings. They are both sincerely trying to find their way through a difficult ironic situation. Their comments, though carrying irony, are not intended to hurt or in any way injure the other. Their remarks are not sarcasm, although the one exchange about "white elephants" might be construed as sarcasm veiling their mutual frustration. Hemingway creates the effect of sarcasm by having the man attack his own defense:

 "No, you wouldn't have."
 "I might have," the man said. 'just because you say I wouldn't have doesn't prove anything."

The primary irony of the situation is that Jig and the American were having a great time. They were touring around, seeing sights, thinking they had the whole world before them and all the time in the world to enjoy being young and free. Then, at the height of their enjoyment, they find out that Jig is pregnant. Hemingway creates this irony by giving glimpses of the fun things and travels they had been engaged in: "There were labels on them from all the hotels where they had spent nights." Part of the irony is that now they have to stop their high-life ways and make a decision. The other painful irony is that, no matter what they decide, their lives will be changed so dramatically as to be shattered.

When you ask about tone, I'm supposing you mean the character's tone of voice since sarcasm and verbal irony would come from the characters rather than the objective, distanced narrator who is sympathetic to both parties. The American's tone of voice is strained but gentle, controlled, and compassionate,. Yet it is ernest in hoping to persuade while, nonetheless, denying intentions of persuading. He does both (persuade and deny) because he truly sees his duty to protect Jig and care for the baby--though he does not like the idea.Hemingway creates this primarily by the man's repetition of sympathetic understanding:

     "You don't have to be afraid. I've known lots of people that have done it."
     "So have I," said the girl. "And afterward they were all so happy."
     "Well," the man said, "if you don't want to you don't have to. I wouldn't have you do it if you didn't want to. But I know it's perfectly simple."

Jig's tone of voice is resigned yet cheerful. She is trying to be optimistic while continuing to be realistic. Neither have a tone of accusation or blame (except for a second in the note of sarcasm). Neither have a tone of regret or anger. There is a mutual tone of past and present love coupled with a realization of being on the threatening threshold of a precipice of change, whichever decision Jig makes.

"I won't worry about that because it's perfectly simple."
     "Then I'll do it. Because I don't care about me."
     "What do you mean?"
     "I don't care about me."
     "Well, I care about you."
     "Oh, yes. But I don't care about me. And I'll do it and then everything will be fine."
     "I don't want you to do it if you feel that way."