You can cut it with a scythe. When wheat is cut it grows back in a two real-time days (after two server-saves).
When you cut the wheat and look at the tile below it says, "You see wheat. It has just been cut."
When it starts to regrow green it says, "You see wheat. It's not mature yet.."
Wheat is only walkable after it is cut in short yellow and green stages.
1. Get the water into a trough or bucket.