Is there any way to get rid of the sound made when a screenshot is created?

Obviously other than muting the computer. I just want to create a screenshot without having that "camera sound" come out.

Is there a way to disable this sound?

After launching Grab, open preferences (in the menus, click Grab => Preferences) and uncheck "Enable Sound".

A screenshot of the preferences here:

You can turn off user interface sounds, though that will remove the empty trash sound and the like.

I havent tried it, but the file itself resides at /System/Library/Components/CoreAudio.component/Contents/Resources/SystemSounds/system/Grab.aif, you might try moving that temporarily and seeing if you can screenshot still.