What does the apostle Paul mean in Romans 9:3 when he says that he would be “cut off from Christ” for the sake of his people, Israel?

I don’t think Paul is implying that (if it were possible) he would somehow substitute his own election to secure the salvation of “disobedient Israel”; that he’d be willing to vicariously suffer in their place.

Rather, in Romans 9-11 Paul is confronting the unthinkable question of whether God could ever forsake his promises to the true Israel. If God really was to abandon his promises, the thought would be too unbearable to endure. Paul objects that he’d rather share Israel’s fate abandoned fate with them, than live in a world where God’s word simply fails.

Paul’s words here are reminiscent of Moses in Exodus 32:32.

In Exodus 32:9-14 God flaggs with Moses the idea of abandoning his plans for Israel after their sin with the Golden calf. The suggestion is that instead, God could make Moses alone into a great nation. The thought that God could prove unfaithful in the eyes of the nations is too horrible for Moses countenance - if such a thing were to happen he’d rather die along with the rest of Israel.

“Oh, what a great sin these people have committed! They have made themselves gods of gold. But now, please forgive their sin—but if not, then blot me out of the book you have written.” (Ex 32:32)

Paul can relate to Moses’ sentiment here. And yet it quickly becomes clear that Paul knows that God has in fact NOT abandoned his purposes for true Israel (just as was the case in Moses’ day). Paul goes on to demonstrate over the rest of Romans 9-11 that the failure of some Israelites to believe. in no way invalidates God’s faithfulness to his promise.