I'm not understanding your question...
Are you asking about mowing the grain or do you have a grass problem in your plot?
If you are asking if you should mow your grains, I would assume that they were at a light enough rate in your mixture to just act as a nurse crop, so you shouldn't need to worry about it.
If your asking about mowing grass because it is invading your plot, mowing it will not kill it, as it will simply regrow.
Mowing broad leaf weeds will help keep them at bay but grasses are a different animal.
Genesis 27:3 Take your bow and quiver full of arrows out into the open country, and hunt some wild game.....