The Holy Martyr Constantine was born upon the island of Mytilene into a [muslim] family. At the age of 15 he fell ill with smallpox, from which he completely lost his eyesight and awaited death. A certain Christian took him to church and washed him with holy water. They brought him out of the temple completely healthy.
His father died early. His mother married again, but his new father was bad and was a drunk. Because of this he moved to Smyrna with his three siblings. He would go continually to the Metropolis of Smyrna, where he heard and learned the Greek language and the Christian faith.
He decided to flee to the Holy Mountain, but no one accepted him. Then St. Gregory V, Patriarch of Constantinople (who was in exile on Athos), having tested him, baptized him as a Christian in Kavsokalyvia, with the name Konstantinos. In the Skete of the Precious Forerunner, he venerated the precious relics of the new martyrs and he was seized with the desire to imitate their deeds. Having passed time in fasting and prayer close to a spiritual father, he decided to go to Magnesia, to have his sister baptized as a Christian. After the advice of the Fathers, however, he sailed from the Holy Mountain and landed in Kydonies. There he was recognized by some Turk who led him to the Aga. He confessed Christ and then confessed his origin. He was imprisoned and terribly tortured. When they questioned him again, Konstantinos made the sign of the Cross before them, thus demonstrating his immovable faith. Then they again imprisoned him and tortured him in a terrible manner. But the leader, seeing that his efforts were in vain, sent him to Constantinople. There having suffered difficult tortures (which had begun on April 23rd), in the end he was hanged on June 2nd 1819.
(taken from: http://www.holytrinityorthodox.com/calendar/los/June/02-06.htm, with additional information from: http://vatopaidi.wordpress.com/2010/06/02/%ce%bf-%ce%ac%ce%b3%ce%b9%ce%bf%cf%82-%ce%ba%cf%89%ce%bd%cf%83%cf%84%ce%b1%ce%bd%cf%84%ce%af%ce%bd%ce%bf%cf%82-%ce%bf-%ce%b5%ce%be-%ce%b1%ce%b3%ce%b1%cf%81%ce%b7%ce%bd%cf%8e%ce%bd-1819-2/ and http://www.immyt.net/saints/martyrs8.htm)
For another life of the Saint, see: http://www.trueorthodoxy.info/los_stconstantine_former_muslim.shtml.