Saudi Arabia is a net food importer, but some food stuffs it exports. Until 1996 it was a large wheat exporter, before it decided to stop them to save water. Since the decision in 2008 to phase out wheat production by 2016 it imports increasing quantities of the item.
Other stuff is still exported, like olives and cut flowers from Al Jawf or shrimps from Al Leith.
Exports of fresh milk products are important for the bottom line of dairy companies like Almarai and a motion of the Majlis Al Shoura in 2010 to ban them to save water was thwarted by the Minister of Agriculture Balghunaim who argued that dairy production in the Kingdom was not water intensive as it imported its barley feedstock (he conveniently overlooked the water consumption of running a dairy farm like drinking water and cleaning. Also considerable amounts of alfalfa feedstock are produced inside the country and alfalfa is even more water intensive than barley or wheat).
Now there is an attempt to phase out exports of open field vegetables, mainly potatoes, to neighboring GCC countries. It will be interesting to see how food export policies and domestic lobby interests will play out in the future.