Csup has very basic mouse support. Enable it by setting mouse to true in ~/.csup/config.yaml:

mouse: true

If mouse support is enabled, you can move the line cursor by clicking on a line. To open the object at a line, double-click on the line.

Enabling mouse support changes the way the windowing system treats the mouse buttons for cut and paste operations. To select, cut, or paste text from/to the window where Csup is running, you will have to hold down the Shift key while using the mouse buttons.