Trim An Image that is outside an artboard

Hi,

I have a clipped image for a presentation slide that is going to be a .svg file. I've clipped the Twitter logo into an image and offset the image but when I save the file, the excess of the image is saved. How do I save it so everything outside of the artboard size is removed? 

In the image below you can see the wireframe of the image that is outside of the artboard.

Any help would be awesome.