Edit your $GROOVY_HOME/conf/groovy-start.conf and add the following line:

  load !{user.home}/.groovy/grapes/**.jar

After that your @Grab will work as advertised:

  #!/usr/bin/env groovy
  @Grab(group='mysql', module='mysql-connector-java', version='5.1.12')

  import groovy.sql.Sql

  def sql = Sql.newInstance("jdbc:mysql://hostname/database", "username", "password", "com.mysql.jdbc.Driver")
  sql.firstRow("select * from users where id=1")