Mormon has indicated that the people did not repent after he had delivered them from danger and they had opportunity for repentance. Now the Lord confirms that this people has moved away from the Lord. Typically the vengeance of the Lord is expressed outwardly from the covenant people. In this case, it is directed toward them because of their disobedience, and hard-heartedness.
Reference: The opening phrase recalls the New Testament:
Romans 12:19
19 Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord.
The combination of the phraseing of “vengeance is mine” with “I will repay” rather clearly points to Romans as the inspiration for the language of the text. As we have seen in other cases, however, the phrase is used in a different setting, though a similar meaning.