There is instructive symbolism in the blood of the Lord Jesus. Presently, the Lord does not have blood. His tabernacle is sustained by the spirit. When he was a mortal man, his blood sustained him. It was pumped through his body by his heart. The physical heart is a pumping muscle. When we talk about the soul, the actuating link between the body and the spirit, we call it our heart (and sometimes our mind). The soul is what causes the spirit to have dominion over the body. In our lives, we are meant to practice the subjection of our bodies to our spirits. Our eventual destiny is to live in a tabernacle fully sustained by our spirits.
When Old Testament priests conducted a sacrifice, they would splatter the blood of the sacrifice onto the person who brought it. What they were being shown was that the blood of Jesus Christ serves to cover their sins from the judgment of God. Justification is the forgiveness of sins. The Lord's blood paid for all the sins of those who will turn from them to him. The use of blood as an instrument of justification is ironic, given that Adam and Eve inherited blood through the fall as a consequence of their sin. The blood of every man save one is a symbol of their sin. The blood of the Lamb of God is the exception. In being the only blood unpolluted by sin, it is the evidence that all mankind can, in fact, keep God's commandments with perfect obedience. In this way, the blood of every man can be offered up as a clean offering to God if they repent and follow the Lord with all their heart, might, mind, and strength. In this case, the justification of the Lord cleans their blood from its sin.
Some speak of being clean from "the blood and sins of this generation." This is a blessing given to those who, having had their own blood cleaned from their own sins, have worked diligently to preach repentance to others. The Lord pays the price for the sins of all those who will repent and heed him, but those who do not must pay the price of their own sin. In the same way, saviors on Mount Zion bring salvation to those who will repent and heed them, but those who do not will bear the burden of their own sins. The preacher is free from the responsibility of the sins of those he preaches to. He is free from their polluted blood.