Presenting our bodies (lives) to God as a living sacrifice is an integral part of our Christian service.   There are several features of sacrifice recorded in the bible that provides us with a deeper understanding of what our Lord expects from us:

1. God requires sacrifices to be “without blemish”. e.g., Lev 1:3,10; 3:1; 4:3;6:6.
2. Our Lord met this requirement as stated in many parts of the bible including 1 Pet 1:19.
3. God requires us to aim for the same standard in the power of the Holy Spirit. Rom 12:1
4. There are significant consequences to offering blemished sacrifices. Consider for example how God cursed and despised priests who offered blemished sacrifices calling them contemptible (Malachi). Note, that he did this in mercy to remind them of their responsibility to him.
5. The presentation of our bodies as (unblemished) living sacrifices includes all aspects of our life continually – no exceptions.  (1 Cor 6:20)​

The description of Christ as a young lamb as having been slain (Rev 5:6) also helps us understand what it means to present our bodies as a living sacrifice. Notice it shows him standing with the scars of Calvary. If we are to be worthy of him, we are to do the same – that is, take our cross and follow him (Mat 10:38). Consider for example the exhortation and testimony of Paul who in the spirit stated: “I die every day” (1 Cor 15:31) and encouraged each saint to stand, having done all (Eph 6:13).
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The verse below I believe summarises our responsibility and privilege well.