How to Disable SMS on an iPhone
Depending on the details of your cellular service plan, you may find it useful to disable your iPhone's "Messages" app to limit or completely stop incoming and outgoing texts. Disabling this feature may prove useful to parents of teenage iPhone users as a way of controlling texting, or to anyone just looking to reduce their iPhone's monthly data rate. You can disable and enable Messages right from the Settings menu.
Tap "Settings" on your main screen.
Tap the "Messages" tab on the Settings menu. The Messages page will load displaying the texing preferences for your iPhone.
Slide the "MMS Messaging" slider to the "Off" position.