The miracle witnessed during Peter's mission to Joppa was the raising of Dorcas from the dead. According to Acts 9:36-42, Dorcas was a disciple who had died, and the believers in Joppa had prepared her body for burial. Peter was summoned to Joppa, and upon arrival, he prayed over Dorcas's body and told her to arise. Dorcas opened her eyes, sat up, and was presented alive to the believers. The miracle caused many people in Joppa to believe in the Lord.