Any left on the stem will rot quickly and pollute the water. Daffodils, jonquils and tulips should not be placed with other flowers immediately after cutting because their secretions can block the stems of other flowers, causing their vase-mates to collapse. Place them in a separate vase for an hour or two then seal the tips of the stems by dipping them in very hot water before adding them to a mixed arrangement. If flowers develop a bent neck, they probably have an air lock in the stem and are unable to absorb water properly. Recut the stems under water and place them in cool water for a couple of hours.
Most flowers absorb water best if cuts are made between nodes or joints.
This is certainly true of carnations and hydrangeas. Never crush the stems, as the damaged tissue will not absorb water well, and the water will become polluted. Sharp, clean cuts are best. A number of flowers respond well to having the stems scalded for a few seconds. Place the ends of the stem in boiling water for about 20 seconds but be careful to keep the heads out of the steam.