How did Martin Luther justify the separation from the Catholic Church? Even though Luther found great abuses in the  Church of his time, there is the clear idea in the Bible that the Church is one, Jesus even prays that his followers be in unity. ("I pray that they will all be one [...] " John 17:21)

So how did Luther justify separating from Rome?
Martin Luther had not intended to separate from the Catholic Church. His 95 theses, and his conduct immediately after he posted them, were intended to achieve reform in the Catholic Church. When he was excommunicated by Rome, he had to either give up his quest for reform or continue to pursue it outside the Catholic Church.  

Bear in mind that there may never have been a single Christian Church, and there certainly was not just one Church in the time of Luther. We know from Paul's epistles that there were already divisions even in his own time, and of course we now know of the Gnostic Christians. Luther would have known of the Greek Orthodox Church, the Coptic Church and possibly even the Nestorian Church. Perhaps Matthew 16:18, in which Jesus says "... I will build my church", suggests that there should only be one church, although others may say that this is not the only possible interpretation of the passage when read in context.

Martin Luther justified his actions because he believed they were right, in the context of the Church in western Europe at the time he took those actions. If at any time in the future the  Catholic Church wishes to reunite with the Protestant Churches, it is open to the Church to initiate dialogue with those Churches, but for this to succeed it must accept the possibility of genuine change both within and outside the Roman Catholic Church. Martin Luther would have welcomed any such action by the Catholic Church.