From Latin 'excusare' (to free from blame) — literally 'take out of a case,' the mirror of 'accuse.'
To attempt to lessen the blame attaching to a fault or offense; to release someone from a duty or requirement; a reason offered in defense of a fault.
From Old French escuser, from Latin excūsāre (to free from blame, to plead a cause, to exempt from accusation), from ex- (out, away from) + causa (cause, reason, legal case, lawsuit). Latin causa is of uncertain further etymology but may relate to PIE *keh2us- (hitting, occasion) or be a borrowing from a pre-Latin Italic source. To excuse something is to drive a cause out of legal consideration — to remove the accusation by presenting a sufficient
The word 'accuse' is the opposite twin of 'excuse.' Latin 'accusare' means 'to call to a cause' (ad- + causa) — to bring someone into a legal case. 'Excusare' means 'to remove from a cause' (ex- + causa). To accuse is to bring into court; to excuse is to release from it. The same root gives us 'because' — literally 'by cause of.'