Objection 1. It would seem that cursing is not a mortal sin. For Augustine in a homily On the Fire of Purgatory [Serm. civ in the appendix of St. Augustine's works] reckons cursing among slight sins. But such sins are venial. Therefore cursing is not a mortal but a venial Sin.
Objection 2. Further, that which proceeds from a slight movement of the mind does not seem to be generically a mortal sin. But cursing sometimes arises from a slight movement. Therefore cursing is not a mortal sin.
Objection 3. Further, evil deeds are worse than evil words. But evil deeds are not always mortal sins. Much less therefore is cursing a mortal sin.
On the contrary, Nothing save mortal sin excludes one from the kingdom of God. But cursing excludes from the kingdom of God, according to 1 Corinthians 6:10, "Nor cursers [Douay: 'railers'], nor extortioners shall possess the kingdom of God." Therefore cursing is a mortal sin.
I answer that, The evil words of which we are speaking now are those whereby evil is uttered against someone by way of command or desire. Now to wish evil to another man, or to conduce to that evil by commanding it, is, of its very nature, contrary to charity whereby we love our neighbor by desiring his good. Consequently it is a mortal sin, according to its genus, and so much the graver, as the person whom we curse has a greater claim on our love and respect. Hence it is written (Leviticus 20:9): "He that curseth his father, or mother, dying let him die."
It may happen however that the word uttered in cursing is a venial sin either through the slightness of the evil invoked on another in cursing him, or on account of the sentiments of the person who utters the curse; because he may say such words through some slight movement, or in jest, or without deliberation, and sins of word should be weighed chiefly with regard to the speaker's intention, as stated above (Question 72, Article 2).
From this the Replies to the Objections may be easily gathered.
Source: Summa Theologica (New Advent)