The Apostle John indicates that "eternal life" was made manifest in the flesh (1 Jn 1:2). This manifestation in the flesh was made possible because of the Holy Spirit (Lk 1:35). Thus eternal life was incarnated in human flesh, who was Jesus the Nazarene. As a person, he thus subsisted not only in mortal life (blood), but also in immortal life (water).
That is, Jesus equated his eternal life with "living water" (Jn 4:13-14). Those who believed in him would not perish, but would have this eternal life (Jn 3:16 and Jn 3:36).
Thus the person of Jesus subsisted in both his eternal life (water) and his mortal life (blood).
When he died on the cross, his eternal life and mortal life departed from his body. The separation and departure of water and blood from his body, respectively, were the visible evidence that he was dead: that is, eternal life and mortal life departed from his body.
So the person was not only dead physically (separation of body and soul), but the person had also died spiritually, since his eternal life was separated from his humanity. (Eternal life was no longer incarnated in human flesh.) That is, his body entered the grave, and his soul entered rest in Hades (Acts 2:27 and Acts 2:31), but his spirit had returned to his Father that was in heaven (Lk 23:46).
When the Roman soldier pierced his side to see if he had expired, the result was not only the visible evidence that he was physically dead (outflow of blood), but also that the person was also spiritually dead (outflow of water). Remember: the person subsisted in two natures, therefore the person was both physically and spiritually dead. Both water and blood departed his body.
Since the person's eternal life was indestructible (Heb 7:16 in NASB), it was "impossible for death to hold him" (Acts 2:24 in NASB). That is, he died for sins, but the death he suffered was vanquished, and therefore swallowed by eternal life -- so he rose from the dead. In other words, spiritual death is not more powerful than eternal life. Romans 4:25 states that he was raised from the dead "because of our justification" (NASB translation), which means that his eternal life was greater than spiritual death, whose sting ("poison") is sin (1 Cor 15:56). To put it another way, he had reversed the law of death-killing-life (condemnation), to life-killing-death (justification). His resurrection "swallowed" death (1 Cor 15:54). The feat therefore eliminated the condemnation of sin.
So while his blood takes away our sins, it is his water (eternal life) that takes away our spiritual death (1 Cor 15:20-22). The Holy Spirit gives us this eternal life as a free gift, and therefore we are born afresh, or rather we should say "born again" through water and spirit (Jn 3:5).