Let’s look at the verse under consideration and determine exactly what it means to be a living sacrifice. Paul wrote to the Romans in 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.”
First, the concept of sacrifice is not that of a dead sacrifice as in the Old Testament. This would constitute a one time event, since a body may only be killed and offered up once. Rather, we are to be a living sacrifice, that is, offering ourselves continually in service to God. Paul described this lifestyle as yielding ourselves as servants of righteousness (Romans 6:12-22). When I yield my will to God and submit myself to Him, I offer up myself as a sacrifice that His will might be done in my life.
Second, as the sacrifices in the Old Testament required an animal without spot or blemish (Exodus 12:5), so we also are to keep ourselves unblemished and unspotted from the world (James 1:27). This is done by walking in the light (1 John 1:7). Peter reminds us to be holy, for God is holy (1 Peter 1:15-16). Paul says we are to purify ourselves from all filthiness of the flesh and spirit, perfecting holiness in the fear of God (2 Corinthians 7:1). The Hebrew writer said without holiness, no man shall see God (12:14).
Finally, we see this presentation of ourselves is our reasonable service. A life of holiness requires dedicated service to God to the best of one’s ability. The concept of service here has its origins in the early days of Judaism, where members of the tribe of Levi were given various tasks in the duties of the tabernacle. Not everyone was to offer sacrifices, some Levites were in charge of what might be described as less glamorous or menial tasks, but they were necessary to the continuance of the tabernacle and later the temple work. This shows us that no matter what the work we do as part of the church (body), it is profitable and needful in the service of God (1 Corinthians 12:12-27).