I beseech you – beg, urge, encourage, appeal
By the mercies of God – compassion
Present your bodies a living sacrifice – as opposed to a sacrifice of death
Holy, Acceptable to God – pure, without spot or blemish
Your reasonable service – since Christ died for us we should live our lives for him. 2 Corinthians 5:15 and He died for all, that those who live should live no longer for themselves, but for Him who died for them and rose again.