Why are the bread and wine mixed together in the Holy Eucharist during an Eastern Orthodox Divine Liturgy? When and why was the practice of commixture started? What is the theological significance of mixing the two together?
The origins of this tradition can be found as early as 120AD in the practice of fermentum, whereby a piece of consecrated bread was broken off and sent to another community in another place for a separate - yet now connected - Eucharistic celebration, thereby expressing the unity of the Church through communion. (The Roots of the Catholic Tradition)

When this practice of traveling leaven was no longer taken up, a piece of the locally consecrated bread was dropped into the chalice and the tradition was explained through various allegory and metaphor, one of which being: this commixture symbolizes the reunion (resurrection) of Christ’s body and soul which were separated at the cross. (The Century Dictionary and Cyclopedia)

The actual word commixture and this notion that Christ essentially puts his power “on hold” before the resurrection, we find in The Life Hidden or Veiled by the Sacramental Species from Cardinal Cienfuegos (1657-1739):


  This life Christ the Lord Himself as High Priest alone sacrifices and
  offers inasmuch as by the sway of His human will he suspends or
  removes the vital actions miraculously produced, and determines not to
  elicit any further action or to use the instrumental power of
  producing them according to His will, until by a kind of resurrection
  in the commemoration of the resurrection in the commixture of the body
  and the blood He resumes the actual life and free use of instrumental
  power.


In his book A History of The Doctrine of The Holy Eucharist, Vol. 2, Darwell Stone writes this of Cardnial Cienfuegos proposal:


  Upon this opinion he built up a theory that in the Eucharistic
  sacrifices our Lord offers this life of the senses and suspends these
  vital actions until the mystical representation of the resurrection in
  the commixture of consecrated elements at the placing of a fragment of
  the host in the chalice; and that this suspension constitutes the
  sacrifice.


As you may have gathered, this tradition is not exclusive to the Orthodox tradition. It is practiced in the Catholic tradition (at least it was when I was an altar boy 45 years ago) and in the Episcopal tradition as well. (4)