Yes you can, i split them down the middle and have done this for years with good effect and when they get overgrown i cut them back with shears, have done this with many types of grasses with good effect, give them a good water before and after.

Yes as Julien has said. If you can sharpen the spade first to make it a clean cut as possible.

If a spade doesn't do it use two forks back to back to force it apart.