Velischek played for Providence College from 1979 to 1983 and was drafted 53rd overall by the North Stars in the 1980 NHL Entry Draft. He turned pro with the Stars at the end of the 1982-83 season and in the playoffs. In the 1983-84 and 1984-85 seasons Velischek split his time between the Stars and the minors. In 1985 he was accquired by the New Jersey Devils. After spending the first part of the season with the Maine Mariners Velischek became a regular on the Devils for five seasons. In 1990 he was sent to the Quebec Nordiques as part of the Peter Stastny trade.