Concise Bible Dictionary:

This is a “cutting, mutilation,” κατατομή, in contrast to the true circumcision, which is a cutting off. It is a term of contempt for the Judaizing teachers (Phil. 3:22Beware of dogs, beware of evil workers, beware of the concision. (Philippians 3:2)).

Strong’s Dictionary of Greek Words:

from a compound of 2596 and τέμνω (to cut); a cutting down (off), i.e. mutilation (ironically)
KJV Usage:
concision. Compare 609

From Anstey’s Doctrinal Definitions:

A term which the Apostle Paul used to describe those who receive the mark of circumcision in their bodies, but are opposed to what it involves practically (Phil. 3:22Beware of dogs, beware of evil workers, beware of the concision. (Philippians 3:2)). The word literally means “against cutting off.” (“Con” means “against,” and “Cision” means “to cut off.”) It is a cutting at the flesh, but not going so far as to cut off the flesh in a practical and spiritual sense. It stands in contrast to “circumcision,” which is a complete cutting off of the flesh. Hence, “the concision were Judaizing teachers who were against the cutting off of the flesh in practise. These teachers had infiltrated the Christian ranks in Paul’s day and have been a plague to true Christianity ever since. (See Circumcision.)