Patch meshes can't be clipped.
What you CAN do however, is go to Gtk's Plugins menu and find "split patch," I think under BobsToolz. That will split a cylinder into 4 bevels for you (and it can also split other patches). You can then manipulate the vertices however you like (details here (
http://wso.williams.edu/~jshoer/patches.htm)). When you're done, if you want, you can use the "merge patches" plugin to take two adjoining meshes and combine them.