If you want to avoid using data, you need to deactivate data connections 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"
Activate or deactivate data connections
Slide your finger down the display starting from the top edge of your mobile phone.
Tap Network Connections.
Tap Mobile Network.
Tap the indicator next to Data Services to turn the function on or off.
Slide your finger up the display starting from the bottom edge of your mobile phone to return to standby mode.
*Please refer to the BlackBerry website for more information or further support.*