Perhaps Arthur Miller ultimately excluded this scene because, in some ways, it makes Abigail seem somewhat sympathetic, and that would be very confusing for the audience. Miller needs a clear villain, someone on whom the trials can be blamed (like he blamed Senator Joseph McCarthy for the HUAC hearings that ruined careers and livelihoods), and this scene problematizes Abigail's motives. Initially, in act 2, we understand absolutely that Abigail is trying to frame Elizabeth Proctor for witchcraft so that she can have John Proctor to herself. However, when she's alone with John in act 2, scene 2, some thirty-six days later, she says,
My spirit's changed entirely. I ought be given Godly looks when I suffer for them as I do [....]. Why look at my leg. I'm holes all over from their damned needles and pins. The jab your wife gave me's not healed yet, y'know [....]. I think sometimes she pricks it open again while I sleep.
At this point, Abigail seems to be believing her own stories. The stage direction says that John "see[s] her madness now." She complains that George Jacobs comes every night and hits her with his walking stick in the same place; she even claims to have a lump, and she tries to show it to John. A perfectly sane Abigail would recall that she's making these stories up, but an Abigail who has somehow lost her wits would treat the memories like they are real, and this is what she does. She even tells John,
[...] God gave me the strength to call [the townspeople who have judged me] liars, and God made men listen to me, and by God I will scrub the world clean for the love of Him!
She even seems to forget that John still has a wife who will go to trial the next morning and she only "distantly" seems to grasp it when he reminds her; more stage direction says that "she is still grasping for her wits." This Abigail does not seem to be in her right mind, and so it becomes more difficult to blame her for the lies she's telling when she, herself, believes now that they are truths. If she can no longer tell the difference between fact and fantasy, can we blame her for mixing the two up? At any rate, this scene throws her sanity into doubt, making her—potentially—somewhat more sympathetic, and I cannot imagine Miller wanted this result.
In Arthur Miller's play, The Crucible, Act Two, scene two, is generally left out of modern productions of the play. It may be because it was confusing to his audience in presenting a conflicting view of Abigail.
The play was originally written as direct criticism of the "witch-hunt" conducted by Senator Joseph McCarthy, while searching out Communists, mostly among artists: writers, actors, etc. This debacle is known as McCarthyism. The sense of accusing the innocent in the United States at this time parallels what happened in Salem, Massachusetts, when a number of girls accused innocent members of their community of being witches and were believed. Almost twenty people would be killed before the madness was stopped.
The portion of the play left out is:
In the woods, Proctor meets with Abigail. She again tries to seduce him, but he continuously pushes her away, informing her that she must stop all accusations being made against his wife. They argue, and Abigail asks him how he intends to prove that what she is saying is false. He informs her that he fully intends to admit to their affair in court if it comes to it, and the scene ends with Abigail saying, "I will save you tomorrow... from yourself I will save you."
Perhaps Miller leaves this out (which was added after the original play was completed) because it gives us the sense that Abigail is dedicated (in a crazy way) to her love of Proctor. While it may be easy for us to understand her kind of criminal mentality after watching countless cop shows on network television, to the audience watching the play, it may seem confusing.
All along Abigail has been very effective in manipulating the community, the court and the other girls to fall in line with her plans. Seeing her as a scheming young woman trying to do away with her competition (Proctor's wife, Elizabeth) makes more sense sandwiched between the foolishness and the apparent lack of mental acuity that affects all of the adults persecuting these innocent members of the Salem.
The idea of Abigail stating that she will "save" John just doesn't ring true. She has already intimated that no one will believe his confession of their affair. She is not interested in saving anyone but herself. And while the audience would probably buy the fact that in this scene she still would do almost anything to get John Proctor, the sense of doing something to save him from himself is not very believable. Had it been presented as a ploy on her part, perhaps it might have worked.