The CrossFit diet prescription is this:

Eat meats and vegetables, nuts and seeds, some fruit, little starch and no
sugar.  Keep intake to levels that will support exercise, but not body fat.

The manner you choose to implement that prescription is entirely up to you.
The two most popular methodologies are 'The Zone' and 'Paleo', but there are
other choices as well. Many have had success with 'The Primal Blueprint' and
'The Metabolic Diet' as well.  Others have had success with some hybrid
version of one of those.

Here's the bare truth:
Body Composition is all about diet.  Without a proper diet you can exercise
all you want and never achieve your goals. Period.  If you eat and drink crap,
you will look and perform like it too.