The bed is a vegetable bed, and the tears are from chopping it. Some editors make it a leek, which fits just as well.
I’m a wondrous creature, a joy to women and useful to the neighbours. I harm nobody in town except the one who kills me. I stand up tall in a bed, and I’m shaggy underneath. Now and then a farmer’s bold daughter dares to grab hold of me. She rubs my red skin, takes off my head and holds me in a tight place. The girl who pins me down soon feels it: her eye goes wet. What am I?
Give me a hintThe hint
The wet eye is the best clue.