I do the job with a dinner fork. My patio has thyme growing in around the stones & I've just battled encroaching clover! The thyme can take quite a beating, so don't be afraid to really get the fork in there and get both plants loose. You'll see all the clover runners and be able to pull them out. Eventually you'll get to the center of the clover plant, dig it out roots and all with nothing more than a little fork.
I find it very rewarding!

Oh, that is genius. I have a ton of grass coming up in my Claridge Druce and have been wondering how to seperate it out. I think I'll try a fork.