St. Cyprian has a number of passages regarding the Eucharist which are worth exploring. Here's another one from William Jurgens' Faith of the Early Fathers (Vol. 1, #583, p. 232):
Because Christ bore us all, in that He bore our sins, we see that by the water, people are signified, while in the wine, indeed, the Blood of Christ is shown. And when the water is mixed with the wine in the cup, the people are made one with Christ, and the multitude of believers is coupled and joined to Him in whom it believes ("To a Certain Cecil," 63, 13).
The mixing of water with the wine is a way of representing the idea of "communion," of how through the Eucharist we become united with Christ, of how we are given grace, which is a share in Christ's divine life.
St. Cyprian was very concerned with unity with the Church, especially through the bishops and ultimately through Peter and his successors (although, apparently, St. Cyprian had some changing thoughts on the primacy of Roman bishop). He was also concerned about disunity arising from the Roman persecutions; he insisted on the need for reconciliation for those Christians who renounced the faith to avoid martyrdom.
Fr. Edward McNamara has a couple of interesting articles at Zenit News Agency on why water is mixed with the wine at the Consecration.