The Greek here is anathema which in the New Testament had a specific meaning of "something dedicated to evil and thus accursed." In later Christian usage, it gradually took on an association with excommunication.
In Galatians 1:8-9, Paul curses ("let that one be accursed") anyone who preaches the Galatians a gospel different to that taught by Paul himself. Paul seems to have the view that whichever missionary founded a church has proprietary rights as to what is henceforth taught in that church. By contrast, when Paul wrote to the Romans, a church that he did not found and only wished to visit briefly on his way to Spain, he was at pains to demonstrate to the Romans that his teachings about Jesus Christ were in accordance with their own. In Romans 15:20, "so have I strived to preach the gospel, not where Christ was named, lest I should build upon another man's foundation:" This was Paul's quid pro quo.
In Galatians 3:10, Paul is defending his teaching against the Jewish law code. In Galatians 3:1-4, Paul calls the Galatians stupid because they have been informed that Jesus was crucified, and should have faith in what they heard, not in supposed benefits in observing the law. In the second part of verse 3:10, Paul is quoting from Deuteronomy 27:26, which is part of a long list of Mosaic curses. Christopher D. Stanley says, in 'Paul's "Use" of Scripture: Why the Audience Matters', published in As It Is Written (edited by Porter and Stanley), page 150, the primary problem is the apparent conflict between the wording of the quotation and Paul's assertion in the first part of the verse. Where Deuteronomy pronounces a curse on the person who does not continually follow the requirements of Torah, Paul appears to apply the curse to those who seek to comply with the laws of Torah. Stanley says the cited verse fails to support Paul's assertion (and could, in fact, be read as upholding the views of his opponents).
In another context, Paul says (Romans 9:3): "For I could wish that I myself were accursed and separated from Christ for the sake of my brothers, my kin according to the flesh."
In each case, Paul was not talking about a different life. In the first case he was symbolically placing a curse on anyone who crosses him, in the second he was clumsily quoting from Deuteronomy in order to support his teaching against Jewish law, and in the third case he was wishing himself accursed, thereby forfeiting his salvation, if that would bring about the salvation of his fellow-Jews.