The Jehovah's Witnesses believe the miracles of Jesus were real. He was not a magician. The miracles were not illusions or trickery. He did not profit from his God given abilities. He performed miracles because of his compassion for people, and not to prove he was the Christ. However the miracles proved that he was not just another Rabbi or teacher. He was 'the Son of God'. 
Jehovah's Witnesses believe that Jesus preformed around 35 miracles and perhaps even more supernatural feats. Matthew 9:35; Luke 9:11
According to the Jehovah's Witnesses, no one today is able to do the miracles of Jesus and his early followers. JW's cannot believe that miracles and spiritual gifts have God's blessing today.  However we are reassured that after armageddon when God establishes his Kingdom, miracles will again be common place.
They say the Bible is explicit on this matter for these reasons:
Make sure of all things. Get The Facts About The Apostle Paul
1. JW's say that Jesus is the Son of Jehovah. However many critics disagree. They say that Jehovah is very different than the Father of Jesus. Examine the evidence in this article, Jehovah vs Jesus
2. Since JW's believe that miracles and spiritual gifts are not possible according to the Bible, they are afraid to examine any evidence that God might be blessing Christians today like he did when Jesus was alive. The source of modern day miracles, spiritual healings, speaking in tongues, and other unusual phenomena is thought to originate with the God of this world, Satan the Devil. Is the devil real? See Devil
Jehovah's Witnesses are warned that the Devil opposes Jehovah and his organization. The Devil is trying to deceive and trick Jehovah's Witnesses into leaving their religion. It is believed that leaving the Jehovah's Witnesses leads apostates into spiritual darkness and away from God's wonderful light. Fear is a powerful tool that compels JWs to be 'like-minded' and 'speak in agreement' even when they have nagging doubts. See Mind Control.