'anticoagulator' is formed in modern English from the prefix 'anti-' (from Greek anti- meaning 'against') combined with 'coagulator' (from Latin roots), literally meaning 'one that works against coagulation'.

'coagulate' comes from Latin 'coagulare' (from 'coagulum' meaning 'clot'), passed into Medieval/Modern English as 'coagulate'; the negative prefix 'anti-' was attached in English to form 'anticoagulate' and agent nouns like 'anticoagulator' developed in modern technical usage.

Originally the Latin root related to producing or forming a clot ('to curdle' or 'to clot'), but with the prefix 'anti-' the modern formation denotes preventing or opposing that action—i.e., preventing clotting.