Objection 1. It would seem that all anger is a mortal sin. For it is written (Job 5:2): "Anger killeth the foolish man [Vulgate: 'Anger indeed killeth the foolish']," and he speaks of the spiritual killing, whence mortal sin takes its name. Therefore all anger is a mortal sin.
Objection 2. Further, nothing save mortal sin is deserving of eternal condemnation. Now anger deserves eternal condemnation; for our Lord said (Matthew 5:22): "Whosoever is angry with his brother shall be in danger of the judgment": and a gloss on this passage says that "the three things mentioned there, namely judgment, council, and hell-fire, signify in a pointed manner different abodes in the state of eternal damnation corresponding to various sins." Therefore anger is a mortal sin.
Objection 3. Further, whatsoever is contrary to charity is a mortal sin. Now anger is of itself contrary to charity, as Jerome declares in his commentary on Matthew 5:22, "Whosoever is angry with his brother," etc. where he says that this is contrary to the love of your neighbor. Therefore anger is a mortal sin.
On the contrary, A gloss on Psalm 4:5, "Be ye angry and sin not," says: "Anger is venial if it does not proceed to action."
I answer that, The movement of anger may be inordinate and sinful in two ways, as stated above (Article 2). First, on the part of the appetible object, as when one desires unjust revenge; and thus anger is a mortal sin in the point of its genus, because it is contrary to charity and justice. Nevertheless such like anger may happen to be a venial sin by reason of the imperfection of the act. This imperfection is considered either in relation to the subject desirous of vengeance, as when the movement of anger forestalls the judgment of his reason; or in relation to the desired object, as when one desires to be avenged in a trifling matter, which should be deemed of no account, so that even if one proceeded to action, it would not be a mortal sin, for instance by pulling a child slightly by the hair, or by some other like action. Secondly, the movement of anger may be inordinate in the mode of being angry, for instance, if one be too fiercely angry inwardly, or if one exceed in the outward signs of anger. On this way anger is not a mortal sin in the point of its genus; yet it may happen to be a mortal sin, for instance if through the fierceness of his anger a man fall away from the love of God and his neighbor.
Reply to Objection 1. It does not follow from the passage quoted that all anger is a mortal sin, but that the foolish are killed spiritually by anger, because, through not checking the movement of anger by their reason, they fall into mortal sins, for instance by blaspheming God or by doing injury to their neighbor.
Reply to Objection 2. Our Lord said this of anger, by way of addition to the words of the Law: "Whosoever shall kill shall be in danger of the judgment" (Matthew 5:21). Consequently our Lord is speaking here of the movement of anger wherein a man desires the killing or any grave injury of his neighbor: and should the consent of reason be given to this desire, without doubt it will be a mortal sin.
Reply to Objection 3. In the case where anger is contrary to charity, it is a mortal sin, but it is not always so, as appears from what we have said.
Source: Summa Theologica (New Advent)