Your iPhone shot videos use lot of space from the storage of your iPhone. You go for finding out backup options. When you go for backup to your Mac using iTunes, you still have this in your mind that after the Videos are be backed, you still have to sit deleting the backed videos from your iPhone. But, you actually do not need to delete your videos manually now. Follow some simple steps to automatically delete your videos from iPhone once backed to Mac using iTunes.
The step by step process is explained below:

1. Connect your iPhone to the computer using USB Cable. Open iTunes if it does not open automatically.
2. Go to ‘Photos App’. In Photos App, click the ‘Import New’ blue colour button, in the upper right corner.
3. Next to the ‘Import Selected’ box, you can see a ‘Delete Items’ box, with a check Box next to it. This is the box that allows you to automatically delete the imported videos from your iPhone. So hit the check box to turn the feature ON.

This way your videos would be backed to your Mac and automatically be deleted from your iPhone.