Greek Text and English Translation
The Greek text of Col. 2:11 states,
ἐν ᾧ καὶ περιετμήθητε περιτομῇ ἀχειροποιήτῳ ἐν τῇ ἀπεκδύσει τοῦ σώματος τῶν ἁμαρτιῶν τῆς σαρκός ἐν τῇ περιτομῇ τοῦ Χριστοῦ TR, 1550
which is translated as,
in whom you also were circumcised with the circumcision made without hands, by the stripping away of the body of the sins of the flesh, by the circumcision of Christ
Instead of τοῦ σώματος τῶν ἁμαρτιῶν τῆς σαρκός ("the body of [the] sins of [the] flesh"), many manuscripts omit τῶν ἁμαρτιῶν ("of [the] sins"), having τοῦ σώματος τῆς σαρκός ("the body of [the] flesh").
The phrase "the body of [the] flesh" (τὸ σῶμα τῆς σαρκός) also occurs in Col. 1:22 (ἐν τῷ σώματι τῆς σαρκὸς αὐτοῦ) in reference to the Lord Jesus Christ's own body. On the other hand, the phrase "the body of [the] sin" (τὸ σῶμα τῆς ἁμαρτίας) also occurs in Rom. 6:6 and Rom. 8:3, but the genitive noun is declined in the singular number (e.g., τῆς ἁμαρτίας) rather than plural number.
The noun ἀπεκδύσει, the dative, singular declension of the lemma ἀπέκδυσις, is related to the verb ἀπεκδύομαι, which occurs twice elsewhere, both times in the Epistle to the Colossians.
Notably, in Col. 3:9, it is written,
Do not lie to one another, after having stripped off the old man with his deeds.
μὴ ψεύδεσθε εἰς ἀλλήλους ἀπεκδυσάμενοι τὸν παλαιὸν ἄνθρωπον σὺν ταῖς πράξεσιν αὐτοῦ TR, 1550
Could "the body of [the sins of] the flesh" (τὸ σῶμα τῶν ἁμαρτιῶν τῆς σαρκός) which was stripped off in Col. 2:11 be equivalent to the "the old man" (ὁ παλαιὸς ἄνθρωπος) which was stripped off in Col. 3:9?
The apostle Paul uses the phrase "the old man" elsewhere in his epistles.
For example, in Rom. 6:6, he writes,
Knowing this, that our old man is crucified with [him], so that the body of sin (τὸ σῶμα τῆς ἁμαρτίας) may be destroyed, so that we no longer serve sin.
τοῦτο γινώσκοντες ὅτι ὁ παλαιὸς ἡμῶν ἄνθρωπος συνεσταυρώθη ἵνα καταργηθῇ τὸ σῶμα τῆς ἁμαρτίας τοῦ μηκέτι δουλεύειν ἡμᾶς τῇ ἁμαρτίᾳ TR, 1550
Sin Personified - King & Master over the Unregenerate
The apostle Paul personifies sin (thus "Sin"), making it the unregenerate individual's master (κύριος; cp. Rom. 6:14). They are "slaves of Sin" (Rom. 6:17 cp. 6:20) and "serve Sin" (Rom. 6:6), being "sold [into slavery] under Sin" (Rom. 7:14).
A servant (slave) serves (δοῦλος δουλεύει); a master is master over (κύριος κυριεύει).
The body is so-called the "body of sin" because Sin indwells it (Rom. 7:17), reigns in it (Rom. 6:12), is master over it (Rom. 6:14) (and thus owns it), and subjugates it, by Its law which the flesh serves (Rom. 7:25), and by Its lusts which they obey (Rom. 6:12). The unregenerate present their "body parts to Sin as weapons of unrighteousness" (Rom. 6:13). Thus, the apostle Paul wrote (speaking as though unregenerate),
But I see another law in my body parts, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my body parts.
Recall that the unregenerate present their body parts to Sin as weapons of unrighteousness, and in turn, Sin uses these body parts as weapons to war against the law of God in one's mind.
This "body of Sin" is likewise called the "body of flesh" because "flesh" implies a lack of the Spirit. A body wherein there is a lack of the Spirit is indwelt by Sin instead.
In Rom. 8:9, the apostle Paul wrote,
But you are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man does not have the Spirit of Christ, he is not his.
"The body of sin" in Col. 2:11 is equivalent to "the body of flesh" and also "the old man." These are stripped off by baptism, the circumcision of the Lord Jesus Christ made without hands, when the Holy Spirit indwells the Christian, and the Christian submits to God's law in his mind, "the law of the Spirit of life in Christ Jesus" (Rom. 8:2), and he now walks "according to the Spirit" (κατὰ πνεῦμα) and no longer "according to the flesh" (κατὰ σάρκα), and invests himself with "the new man" (Col. 3:10).