Who does Paul say were "cut (broken) off"? Doesn't Paul say all of Israel will be saved?
You seem to be missing the point Prentis. Your not applying the whole premise here by using only part of it, the "cutting off" and then ignoring the "grafting back in" which is part of the same context. To apply one without the other is to ignore context and misapply.
Read further down, verse 32, "for God has imprisoned everyone in disobedience so he could have mercy on everyone". Now whatever meaning you apply to the "cutting off" must not conflict with verse 32 to keep things within the proper context.
Take a slow deep breath and condition yourself to just think about all that I say here before you decide how to answer it jiggyfly. Don't let your mind jump ahead to what you think your defense will be because you have plenty of time for that after you follow the full flow of the thoughts I will present to you.
Sticking only to Romans 11: 13-14 notice that Paul was not thinking all would be saved, but only some of them:
Romans 11:13 "For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office:
14 If by any means I may provoke to emulation them which are my flesh,
and might save some of them."
Remember why Paul said they fell:
11 "I say then, Have they stumbled that they should fall? God forbid: but rather through their fall salvation is come unto the Gentiles, for to provoke them to jealousy."
Did Paul mean that they would all be provoked to jealousy and so repent? No, that is the same thing he talked about wanting to do in verses 13-14. And there he said it would only be some of them.
So then there other statements he made that you are reading more into than is there. And to lay the groundwork to discuss them lets first look through the the context of chapters 9 and 10 to see what we can learn about Paul's expectation concerning the saving of all Israel, whether it would be all or just some as we saw in verses 13-14.
Romans 10:1 "Brethren, my heart's desire and prayer to God for Israel is,
that they might be saved."
Paul was a man of such strong faith that he rejoiced in his trials and tribulations on behalf of Christ and the brethern in Christ. If his fleshly brothers who had been blinded were suffering for the cause of Christ and would yet be saved Paul would have rejoiced in that also. It would have been a lack of faith to know they would eventually be unblinded and then yet to lament them as he did here, as follows:
Romans 9:1 "I say the truth in Christ, I lie not, my conscience also bearing me witness in the Holy Ghost,
2 That I have great heaviness and continual sorrow in my heart.
3 For I could wish that myself were accursed from Christ for my brethren, my kinsmen according to the flesh"
But Paul knew this concerning the some he hoped to save, as follows:
Romans 9:6 "Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel:
7 Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called.
8 That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed."
Paul was trying to get the idea out of the minds of the gentiles that God had accursed the entire race for the death of Christ. That is because Paul was preparing their hearts and their minds to be the preachers that would go to his fellow Jews and do as he said at Romans 11:14 "If by any means I may provoke to emulation them which are my flesh, and might save some of them."
And we see that very strong in chapter 10 of Romans:
Romans 10:14 "How then shall they call on him in whom they have not believed? and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher?
15 And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!
16 But they have not all obeyed the gospel. For Esaias saith, Lord, who hath believed our report?
17 So then faith cometh by hearing, and hearing by the word of God.
18 But I say, Have they not heard? Yes verily, their sound went into all the earth, and their words unto the ends of the world.
19 But I say, Did not Israel know? First Moses saith, I will provoke you to jealousy by them that are no people, and by a foolish nation I will anger you.
20 But Esaias is very bold, and saith, I was found of them that sought me not; I was made manifest unto them that asked not after me.
21 But to Israel he saith, All day long I have stretched forth my hands unto a disobedient and gainsaying people."
He was then and there preparing the preachers to fulfill that prophecy concerning provoking them to jealousy.
You have the right interpretation of Romans 11:32 as I think I read of your post. They are saved as we are saved. Romans 11:32 is almost a shadow of Galatians 3:22. they both are saying essentially the same thing, especially when you know the word they does not actually appear in the original language text of Romans 11:32.
Because this is getting long i will talk about the rest of chapter 11 later showing how these are just things Paul was saying could happen if the Gentiles failed to appreciate the purpose of the grace shown them.
And when he says that in that manner all Israel will be saved it should be understood as per what he said at Romans 9:6-8, "all" as in all who really are the elect of Israel by faith.
There are places in Paul's writings where we can go that he discusses sowing that small seed of faith to the remnant that were yet out there among the Jewish population, even as there were yet Gentiles needing to have that seed of faith yet sown.