The immediate context explains why Paul mentions the “mouth” and the “heart” in this specific passage, but it also raises a new question. Why did Paul have to make an argument from the Old Testament that salvation was by grace through faith? Was there anyone who doubted this? Reading Romans as an entire book explains the reason for each passage within that book. Paul is addressing a controversy between Jewish and Gentile Christians.
Paul begins Romans by emphasizing that the Gentiles are lost (Rom 1:18-32); just as the Jewish Christian readers are applauding, Paul points out that religious people are also lost (Rom 2), and summarizes that everyone is lost (Rom 3). Paul establishes that all humanity is equally lost to remind us that all of us have to come to God on the same terms; none of us can boast against others.
But most Jewish people believed that they were chosen for salvation in Abraham; therefore Paul reminds his fellow Jewish Christians that it is spiritual rather than ethnic descent from Abraham that matters for salvation (Rom 4). Lest any of his Jewish readers continue to stress their genetic descent, he reminds them that all people—including themselves—descend from sinful Adam (5:12-21). Jewish people believed that most Jews kept all 613 commandments in the law (at least most of the time), whereas most Gentiles did not even keep the seven commandments many Jews believed God gave to Noah. So Paul argues that while the law is good, it never saved its practitioners, including Paul (Rom 7); only Jesus Christ could do that! And lest the Jewish Christians continue to insist on their chosenness in Abraham, Paul reminds them that not all Abraham’s physical descendants were chosen, even in the first two generations (Rom 9:6-13). God was so sovereign, he was not bound to choosing people on the basis of their ethnicity (9:18-24); he could choose people on the basis of their faith in Christ.
But lest the Gentile Christians look down on the Jewish Christians, Paul also reminds them that the heritage into which they had been grafted was, after all, Israel’s (Rom 11). God had a Jewish remnant, and would one day turn the majority of Jewish people to faith in Christ (11:25-26). And at this point Paul gets very practical. Christians must serve one another (Rom 12); the heart of God’s law is actually loving one another (13:8-10). Ancient literature shows that Roman Gentiles made fun of Roman Jews especially for their food laws and holy days; Paul argues that we should not look down on one another because of such minor differences of practice (Rom 14). He then provides examples of ethnic reconciliation: Jesus though Jewish ministered to the Gentiles (15:7-12) and Paul was bringing an offering from Gentile churches for the Jewish Christians in Jerusalem (15:25-31). In the midst of his closing greetings, he offers one final exhortation: Beware of those who cause division (16:17).