Instead of drawing a graphic to use as a clip, use a tool to create a featureset which is created interactively just like a graphic when setting up parameters to run the tool.
If you have hundreds of graphics that should have been features, there is a menu item to turn graphics to features. You can then select a real feature from a featureclass to use it as a clip.
Just don't use graphics as features, they are really most suitable for illustrations of non GIS data in a layout.
