If you want to avoid using data, you need to deactivate mobile data on your mobile phone. Once done, you can only make voice calls, send SMS and use applications that don't require an internet connection.
Find "Mobile Network"
Turn mobile data on or off
Slide your finger downwards starting from the top edge of the display.
Tap Network and Connections.
Tap Mobile Network.
Return to the home screen
Tap the indicator next to "Data Services" to turn the function on or off.
Slide your finger upwards starting from the bottom edge of the display to return to the home screen.
*Please refer to the BlackBerry website for more information or further support.*