The truth is that the Bible very explicitly speaks of this distinction, and that many protestants do believe in it even if they do not call it “mortal” and “venial” sin. To begin with, we must clear up one extremely common misunderstanding. Many people, both Catholic and protestant, think that a mortal sin is something that is a “really bad” wrongdoing whereas a venial sin is something that is a minor wrongdoing. For instance, a common minunderstanding would be that murder is a mortal sin because it is a really bad thing, whereas telling someone to go to hell would be a venial sin because it is a more minor act. This is not true at all. What then is true?
The essence of what mortal sin is is summed up by Hebrews
10:26-27 - "For if we go on sinning deliberately after receiving the knowledge of the truth, there no longer remains a sacrifice for sins, but a fearful expectation of judgment, and a fury of fire that will consume the adversaries. This is what mortal sin is - the deliberate act of sinning when one knows that it is wrong.
The general protestant view is Christ’s sacrifice was sufficient for our forgiveness, and that through our faith Christ forgives us all our sins whatever they may be. This is in fact also the Catholic view. We are all going to sin, but when we do, we have an advocate in Christ who is the propitiation for our sins (1 John 2:1-2). The distinction is that Catholics realize that one can sin deliberately, as Hebrews points out. Christ always said that we must repent. He expects this of us. One who sins deliberately is not repentant, but defiant. Even in Old Testament times, there was a distinction between a sin commited out of weakness and one commited defiantly:
“If one person sins unintentionally, he shall offer a female goat a year old for a sin offering. And the priest shall make atonement before the LORD for the person who makes a mistake, when he sins unintentionally, to make atonement for him, and he shall be forgiven. You shall have one law for him who does anything unintentionally, for him who is native among the people of Israel and for the stranger who sojourns among them. But the person who does anything defiantly, whether he is native or a sojourner, reviles the LORD, and that person shall be cut off from among his people. Because he has despised the word of the LORD and has broken his commandment, that person shall be utterly cut off; his iniquity shall be on him.” - Numbers 15:27-31
Hebrews tells us that if a person, who knows something is wrong, does it deliberatley instead of out of weakness, then there is no sacrifice remaining for that persons sin, and he can expect judgement and fire. This is mortal sin; it is a sin done defiantly, a sin in which a person says, “I know this is wrong, and I am strong enough to avoid this, but I don’t care that it is wrong, and I don’t care that it offends God, and I am going to do it anyways.” In this case, the person is not repentant, and the person is in defiance of God, and Christ’s sacrifice will not atone for the sin because the person is essentially rejecting that forgiveness.
This is why John writes, “If anyone sees his brother committing a sin not leading to death, he shall ask, and God will give him life–to those who commit sins that do not lead to death. There is sin that leads to death; I do not say that one should pray for that. All wrongdoing is sin, but there is sin that does not lead to death.” (1 John 5:16-17). He is explaining that we can pray to Christ and He will forgive us and our brothers our sins, but that our prayers cannot help one who has sinned “unto death,” and has rejected Christ’s salvation and is in defiance of God. Mortal sins are called “mortal sins” because they are, as John writes, “unto death,” they cause spiritual death. The term venial sins does not so much refer to a different class of sins as it refers to any and all sins which are not done defiantly. The word venial means “easily excused or pardonable,” which is why is it the word used to desribe these sins.
So it is easy to see where the two requirements of full knowledge and full will are found in Scripture: they are very explicit in Hebrews 10:26. Grave matter is also visible rather readily in Scripture. In John 19:11I, Jesus indicates that some sins are worse than others. In Galatians, 1 Corinthians, and Ephesians, Paul provides lists of sins which will bar persons from heaven. He lists various acts which are of grave matter. When Christ is asked what commandments must be followed to make it to heaven, he responds by citing those commandments which point to grave matter (Matthew 19:16-19). Earlier in Matthew, Jesus gives an example of one sin (a minor insult) that might get a minor punishment, and of another more grave sin (a hateful curse) which might send a person to hell. (Matthew 5:21-22)