Question: “Romans 1:18-28: what does the scripture try to convey in this verse: ‘he gave them over to a depraved mind’? How does this fit in with the idea of grace?”

Answer: Paul is conveying in this verse that God has removed all common grace from these individuals and allowed them to run to the fullest extent of their depravity. Implicitly we understand that though all people are totally depraved, not all are utterly depraved. In other words, though people cannot save themselves because of their pervasive sinfulness, God does extend grace even to the unregenerate so that they can do decent things and are restrained from the vilest deeds. When He removes that common grace, people will be as bad as they can be.

Thus in answer to the question of how this verse fits in with the idea of grace, I can answer that there is no grace here at all; God has withdrawn it. But who are the people under consideration? Paul is discussing idolaters, people who know that there is a God through the evidence in nature but refuse to worship Him as God. Instead they make idols and worship them. This is blatant rebellion against God. They have deliberately chosen to reject God, and so God chooses to reject them and let them go their chosen way. Paul is in no way discussing a believer in God or anyone who might be seeking salvation. God does not withdraw all grace from such people. But by withdrawing common grace from idolaters God demonstrates what happens when people truly reject God and say that they do not need Him. He lets it be known what the result is by listing several terrible sins. His list is exemplary and not exhaustive of possible sins.

There is certainly a warning here against rejecting God, but there is a deeper warning against presuming on the grace of God. Anytime God extends grace we cannot view it as an obligation for God. God will show mercy on those on whom He so wills to show mercy. If grace is extended to us today, we need to accept it now, for there may well come a time when it is not extended. At that point the person will no longer be interested in God and His grace at all, for where there is no will, there is no grace.