There is much to be said about the Mass and Communion but I will limit my response to the question asked.
When we talk of receiving the body and blood of Jesus, we mean that we receive Christ totally in his humanity. Christ cannot be divided, so he is fully present as human and divine in both species.
Body and blood not separate
In other words, Christ's body and blood can no longer be separated; we receive him completely whether we partake of the consecrated bread with or without the cup. That is why, for centuries, the Church had no problem with reception of the consecrated bread alone, although reception under both species is recommended now.
It may seem that we emphasize the blood but that is because Christ shed the last drop of his blood for us in his death on Calvary. Christ gave himself to us in the ordinary elements of food and drink at the Last Supper prior to the culmination of his giving of himself to death on the cross.
The evangelists give us Jesus' words: "This is my blood which will be shed for you" separately from: "This is my body given up for you." Therefore, we do separate consecrations at Mass although Christ is fully present in both.
That death was bloody but the Mass is an unbloody sacrifice.
Christ died once and for all and he cannot die again.
The Catholic Catechism states: "The sacrifice of Christ and the sacrifice of the Eucharist are one single sacrifice. Only the manner of offering is different. In this divine sacrifice which is celebrated in the Mass, the same Christ offered himself once in a bloody manner on the altar of the cross, is contained and is offered in an unbloody manner" (no. 1367).
The Church has continued to follow Christ's "Do this in remembrance of me" since the beginning. The moment of Consecration is surrounded with readings, prayers and hymns because that is what the early Christians did.
Justin Martyr in the middle of the second century writes that they gathered on Sunday, reading the memoirs of the Apostles or the writings of the prophets followed by the presider's discourse. Prayers were said for the world, followed by the Eucharistic Prayer with the consecration and the reception of Communion.
One Body of Christ
As human beings, we need to give honour and glory to God in a communal liturgy which feeds us with the Word of God in Scripture and with Christ's body and blood.
As the one Body of Christ, a community of disciples, together we need to join ourselves, our prayers and sacrifices to Jesus' sacrifice on the cross, thus entering more fully into a spirit of gratitude to God for the gift of Christ's presence in our hearts and our lives and in the world.