When the petals on the tulip blooms begin to wilt and fall of the stem you can start the cleanup process. The blooms widen and one by one the petals begin to fall off until just the stem, topped off by the seed pod remain. Instead of cutting off the stems on the bulbs, just remove any seed heads on your tulips that were pollinated during the spring. Unless you're engaged in a tulip hybridizing program, and want to collect tulip seeds, there's no need for your tulips to produce a seed pod. In fact, your tulip bulbs will focus their energy on feeding the seed pod to produce viable seeds negatively affecting next year's bloom. Deadhead any tulip seed pods for healthier bulbs and more blooms next year.