1) to throttle, strangle, in order to put out of the way or kill
2) to hang one's self, to end one's life by hanging
Part of Speech: verb
From G575 and ἄγχω agchô (to choke; akin to the base of G43); to strangle oneself off (that is, to death): - hang himself.
These two sites give similar information, with the definition from several dictionaries and statistics on the use of the word.
Perseus Digital Library
University of Chicago's Logion lexicon
Thayer's dictionary plus other information.
From this site's dictionary (in Italian)
Click on the first column to search for that word as a form of the root ἀπάγχομαι; click on the second column to search for that grammatical form of the root ἀπάγχομαι; click on the third column to search for that word and grammatical form; click on the total to search for the root ἀπάγχομαι.