Definitely, don't pull it off.
I've done it several times using the method described by Daniel Knop, with 100% success. It's important to learn how to do this whenever the need arises (e.g. remove pyramid snails, redecorating, etc.).
As long as you can visibly see the byssal threads, you're OK. You can't perform this by touch, alone.
Find a small blade (something just as sharp as a swiss army knife). You can slightly lift up the clam a couple of degrees to get an angle, but no more than that. Use the knife to cut off the thread as close to the rock as possible, and you will avoid doing any damage to the byssal gland.
Now, enjoy your clam.