First look at the meaning of καταργέω:
καταργέω ... ① to cause someth. to be unproductive, use up, exhaust, waste of a tree κ. τὴν γῆν Lk 13:7 (cp. ἀργεῖ οὐδὲν ἀλλὰ καρποφορεῖ OdeSol 11:23).
② to cause someth. to lose its power or effectiveness, invalidate, make powerless fig. extension of 1 ... τὰ ὄντα κ. nullify the things that (actually) exist 1 Cor 1:28. τὸν νόμον make the law invalid Eph 2:15; cp. Ro 3:31 ... ③ to cause someth. to come to an end or to be no longer in existence, abolish, wipe out, set aside τὶ someth. τὰ τοῦ νηπίου set aside childish ways 1 Cor 13:11.... ④ to cause the release of someone from an obligation (one has nothing more to do with it), be discharged, be released.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). In A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 525-526). University of Chicago Press.
While BDAG puts both verses with the meaning of (2), the context points to Eph. 2:15 having the meaning of (4), thus two different meanings for καταργέω.
The context is "he himself is our peace" in v14. We need to overcome what the English word for peace means to what שָׁלֵם means in the Old Testament law.
See Is the term שָׁלֹום (peace) in Isaiah 53:5 usually misunderstood?
Tetelestai - What did Jesus really say in John 19:30 assuming he spoke Aramaic or Hebrew?
Thus, Eph. 2:15 means Jesus Christ released us from the legal obligation of the Old Testament law by being the sacrifice for our sins. However, as in Rom. 3:31, he did not abolish the law but fulfilled it for us. In Romans 3 Paul wrote that sin is still valid (Rom. 3:23). In Eph. 2:15 Paul wrote that Jesus Christ paid the restitution for the Law.