Your bodies refers to the whole person as they live in the world, not only the physical body.
on account of God’s mercy: This refers to everything Paul explained in chapters 1–11.
which is your spiritual service of worship (or which is your reasonable service): This phrase has at least three possible meanings:
Our sacrifices are reasonable considering all of God’s acts of mercy.
Our sacrifices are spiritual, not the offering of an animal but of ourselves in spiritual service.
Our sacrifices are intelligent, offered with full awareness of God’s goodness to us.