Spider Mites

Don’t worry about the cut stems. They will dry up. The webbing on your plant could be spider mites. We’ve included a link so you can see what these little sap sucking spider-like organisms look like, but at this stage of damage, you may want to remove the affected leaves and treat with an appropriate pesticidal product as recommended below, or in the web link provided. For future reference, if you catch the problem before it gets too bad, you can control them by spraying with neem oil or pesticidal soap, which can be purchased at most garden centers. Be careful to read the labels and apply any of these types of products properly. Be careful to spray the undersides of the leaves, the stems, and the tops of the leaves. Repeat the application as recommended on the product label to kill any new mites that hatch from eggs afer the first application.
http://www.ipm.ucdavis.edu/QT/spidermitescard.html