Somebody who knows more may step in and contradict me...but I think the scapes also draw in food for the bulb(while they are still green). However, I often use tulips for cut flowers, and my tulips are still multiplying even when I cut the scapes off, so if you think they look pretty ugly, I don't think cutting them will make or break your tulips next year.

Just don't let them set seed pods, whack those babies off. It keeps the plants energy in the bulb not in reproduction.

Cut the flower stock to the level of the leaves. Leave the leaves until they are brown and they can easily be pulled. If you have to tug on the leaves the bulb is still using them. Last year after I pulled the leaves I lifted a couple of clumps and threw in a hand full bone meal and I got huge blooms this spring. Im planning on doing a few more this way this year if I have time. Cheryl