A Living Sacrifice
Can something that is sacrificed go on living? Yes, when the term is used to refer to the people of God "putting to death" old ways and attitudes and thereafter living a life of genuine obedience to God.
"12:1 I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service.
12:2 And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God." (Romans 12:1-2 KJV)
"Be ye transformed by the renewing of your mind, that ye may prove what is that good"
Becoming a true Christian doesn't mean living a lawless life, as some seem to think (see Grace Into Licentiousness). Christianity means being liberated from Satanic lawlessness: "yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God."
"6:1 What shall we say then? Shall we continue in sin, that grace may abound? 6:2 God forbid. How shall we, that are dead to sin, live any longer therein? 6:3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? 6:4 Therefore we are buried with him by Baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
6:5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection [see When Will You Be Judged? and Could Christ Return Tonight?]: 6:6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin. 6:7 For he that is dead is freed from sin.
6:8 Now if we be dead with Christ, we believe that we shall also live with him: 6:9 Knowing that Christ being raised from the dead dieth no more; death hath no more dominion over him. 6:10 For in that he died, he died unto sin once: but in that he liveth, he liveth unto God.
6:11 Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord. 6:12 Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof. 6:13 Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God. 6:14 For sin shall not have dominion over you: for ye are not under the law, but under grace." (Romans 6:1-14 KJV)
A living sacrifice means living a way of life, no longer "living" (actually, perishing from) the ways of the world that produce only misery and death.
"4:21 If so be that ye have heard him, and have been taught by him, as the truth is in Jesus:
4:22 That ye put off concerning the former conversation the old man, which is corrupt according to the deceitful lusts; 4:23 And be renewed in the spirit of your mind;
4:24 And that ye put on the new man, which after God is created in righteousness and true holiness.
4:25 Wherefore putting away lying, speak every man truth with his neighbour: for we are members one of another. 4:26 Be ye angry, and sin not: let not the sun go down upon your wrath: 4:27 Neither give place to the devil. 4:28 Let him that stole steal no more: but rather let him labour, working with his hands the thing which is good, that he may have to give to him that needeth.
4:29 Let no corrupt communication proceed out of your mouth, but that which is good to the use of edifying, that it may minister grace unto the hearers. 4:30 And grieve not the holy Spirit of God, whereby ye are sealed unto the day of redemption [see Conceived Again]. 4:31 Let all bitterness, and wrath, and anger, and clamour, and evil speaking, be put away from you, with all malice: 4:32 And be ye kind one to another, tenderhearted, forgiving one another, even as God for Christ's sake hath forgiven you." (Ephesians 4:21-32 KJV)
Fact Finder: Why was the Christ sacrificed?
See Why Blood?