Paul says many things in the book of Romans. The entirety of Romans chapter six is very instructive when it comes to sin. For the sake of brevity, I will condense things by using a selected set of verses for purposes of summary.
In verse 1 and 2 Paul tells us that we are forbidden to sin. He says:
“WHAT SHALL we say then? Are we to continue in sin that grace may abound? By no means! How can we who died to sin still live in it?”
Paul then tells us in verse 6 and 7 that:
“We know that our old self was crucified with him so that the sinful body might be destroyed, and we might no longer be enslaved to sin. For he who has died is freed from sin.”
Since we are born again and live in the Spirit we are freed from committing sin. This point is also made by Jesus in John 8:33-36.
Then in verses 10 and 13 Paul goes on to say:
“The death he died he died to sin, once for all, but the life he lives he lives to God. So you also must consider yourselves dead to sin and alive to God in Christ Jesus.” Let not sin therefore reign in your mortal bodies, to make you obey their passions. Do not yield your members to sin as instruments of wickedness, but yield yourselves to God as men who have been brought from death to life, and your members to God as instruments of righteousness."
Then in verse 16 Paul tells us what happens if we yield ourselves to sin. This is what he says,
“Do you not know that if you yield yourselves to any one as obedient slaves, you are slaves of the one whom you obey, either of sin, which leads to death, or of obedience, which leads to righteousness?”
Paul reiterates this again in verse 23 by saying,
“The end of those things[sins] is death.”
Paul also lists the things that fall into the category of sins that lead to death. An example of this is found in Galatians 5:19-21 which says:
“Now the works of the flesh are plain: fornication, impurity, licentiousness, idolatry, sorcery, enmity, strife, jealousy, anger, selfishness, dissension, party spirit, envy, drunkenness, carousing, and the like. I warn you, as I warned you before, that those who do such things shall not inherit the kingdom of God.”
You can also read about mortal sin in 1 John 5:15-17. Some translations use the phrase “sin unto death” in place of the word “mortal.”
I hope this helps.