'screw-up' is formed in modern English by combining the verb/adjective 'screw' with the particle 'up'. The colloquial phrasal verb 'screw up' (meaning 'to make a mistake' or 'to ruin') developed in the 20th century, and the hyphenated noun 'screw-up' (meaning 'a mistake' or 'a person who messes up') is derived from that usage.

'screw' as a verb and noun has older roots (originally related to twisting or turning), but the sense 'screw up' meaning 'to botch or ruin' arose in informal American and British English in the early to mid 20th century; by mid 20th century the noun 'screw-up' was recorded for both 'a mistake' and 'a person who makes mistakes.'

Originally 'screw' related to twisting or tightening; over time the verbal phrase 'screw up' took on a figurative sense 'to spoil, ruin, or make a mess of something,' and the noun 'screw-up' came to mean both the error itself and the person responsible.