Living Sacrifice = Christian Undead Zombies?

What does it mean to be a living sacrifice? This question has split churches, but we asked it anyway at mid-week Bible study. We genuinely want to know and we believe the Holy Spirit wants to teach us. Here is the key text in question:

Romans 12:1,2

¹Therefore I urge you, brethren, by the mercies of God, to present your bodies a living and holy sacrifice, acceptable to God, which is your spiritual service of worship.

 ²And do not be conformed to this world, but be transformed by the renewing of your mind, so that you may prove what the will of God is, that which is good and acceptable and perfect.

More Later...