Given our new identity in Christ (3:1-4), we are to mortify earthly vices (3:5). Unlike the disobedient who provoke God (3:6), we put away all such sins.
All Such Sins (8-9a): Paul develops the earlier list of five vices and calls us to "remove all such sins,"[1] and that proactively.[2] He also adds to that list five more: "anger, wrath, malice, slander and abusive speech." These highlight sins against God in interpersonal relationships. Furthermore, we are called to no longer "lie to one another." "All liars" will be condemned (Rev. 21:8), and we who are heaven-bound pursue Christ's standard of integrity (Matt. 5:20, 37).
Old and New Man (9b-11): We get rid of these sins, "since you have put off[3] the old man" and "have put on the new man."[4] This twofold action describes our past decision[5] to follow Christ. At conversion, the believer took off the old man with "its evil practices," and willingly dressed himself with the new man.[6] In the new man,[7] we are being renewed according to Christ (3:10)[8] and He is all things (3:11) to us. Such things as race, ceremony, culture and status[9] are now trivial. Christ is "in all believers," and this is what governs our fellowship.
[1] The imperative "put aside" is literally "put away," or "remove." "Them all" is literally "all the things." Given the earlier list of sins, this is properly "all such sins" (NET, "all such things"), pointing back to that earlier list.
[2] NKJV's "you yourselves are to put off" accurately reflects the middle voice (our active role). Cf. 2 Pet. 1:5-10.
[3] These two verbs are parallel ("have put off… have put on" [ESV]) which relate to clothing. This is like taking off work clothes and getting dressed for a wedding. Only a fool would now do yard work dressed like this.
[4] NASB's "old self" is literally "old man," and "new self" is best understood as "new man" (per NET, NKJV).
[5] This was past ("since") and it was our decision, as the two middle voice verbs (so in Greek) points out.
[6] This was the willing decision of the believer. It is senseless to return to the old lifestyle (cf. 2 Pet. 2:20-22).
[7] "A renewal in which" is literally "where" (NKJV). 3:11 further defines the new man not the renewal per se.
[8] "One who created" is the Father, whose "image" is Christ (1:15). The created thing ("him") is the new man. The purpose of renewal is stated as "a true knowledge." This aim is stated elsewhere (1:9; 2:2; Eph. 4:13).
[9] Greek/Jew is race. Circumcision is ceremony. Barbarian/Scythian is culture. Slave/freeman is social status.