1) to pluck out, draw out, i.e. root out
2) to choose out (for one's self), select, one person from many
3) to rescue, deliver
Part of Speech: verb
From G1537 and G138; active voice to tear out; middle voice to select; figuratively to release: - deliver, pluck out, rescue.
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 ἐξαιρέω; click on the second column to search for that grammatical form of the root ἐξαιρέω; click on the third column to search for that word and grammatical form; click on the total to search for the root ἐξαιρέω.