I agree with Arlene, re-locate the asparagus to a new bed, and then kill off the Johnson grass. If the grass is contained in the raised bed and can't grow under the edges, I'd cover it tightly with a thick black plastic tarp, and let it like that for a year or two. If it can escape, you may be forced to use something like Round Up on it, and then I'd still cover it for at least a year before using it again for food. Once the Johnson grass is dead, you could alway replace the soil in the bed if you don't want to use it for food, and put it someplace like a flower bed somewhere.
