to place under a curse: to declare in solemn words that someone, most often the speaker himself, is handed over to God for destruction
The weight of this word comes from the noun behind it, the biblical term for something devoted to destruction (ἀνάθεμα). In the Greek Old Testament that noun stood for the Hebrew ban (חרם): a person, city, or object taken out of ordinary use and handed over to God, in war usually by being destroyed. So this is not a general word for cursing. To speak it over someone is to consign that person to ruin at God's hands.
In Acts the people who say it are cursing themselves. More than forty men bound themselves neither to eat nor to drink until they had killed Paul, and the oath they swore called destruction down on their own heads if they failed. Acts 23:14 piles the word on itself for force, something close to "with a curse we have cursed ourselves."
Mark 14:71 is different, and it is the only place in the Bible where this verb has no stated object. Peter began to curse and to swear that he did not know Jesus. The verb paired with it there is the ordinary word for taking an oath (ὄμνυμι); this one supplies the curse that makes such an oath binding. Whether Peter called destruction down on himself if he was lying, or cursed Jesus to prove he was no follower of his, is genuinely argued, and both readings have strong defenders. Matthew tells the same scene with a harsher sounding relative of this word (καταναθεματίζω).
Nuances
Whom Peter curses in Mark 14:71, where the verb uniquely has no stated object.
- majorityPeter curses himself, swearing that destruction may fall on him if he is lying: the oath formula behind renderings such as "he began to call down curses on himself."; BDAG, s.v. ἀναθεματίζω; LSJ, s.v. ἀναθεματίζω; Adela Yarbro Collins, Mark (Hermeneia; Minneapolis: Fortress, 2007), 708; Jacek Pietrzak, The Biblical Annals 9/2 (2019), on Mark 14:71
- minorityThe unexpressed object is Jesus: under pressure Peter cursed his master, the strongest available way of dissociating himself from him.; Otto J. F. Seitz, "Peter's 'Profanity': Mark 14:71 in the Light of Matthew 16:22," Studia Evangelica (TU 73, 1959), 516-519; H. Merkel, "Peter's Curse," in The Trial of Jesus: Cambridge Studies in Honour of C. F. D. Moule (London: SCM, 1970), 66-71; G. W. H. Lampe, "Peter's Denial," Bulletin of the John Rylands Library 55/2 (1973); Raymond E. Brown, The Death of the Messiah (New York: Doubleday, 1994), 1:604, 625-626; R. T. France, The Gospel of Mark (NIGTC; Grand Rapids: Eerdmans, 2002), 622