What airfoil simulation software is suitable for a cut trailing edge?
One tool you might want to consider is MIT's XFoil. I'm not sure I fully understand what you'd like to do, but this tool is used in many of MIT undergraduate aerodynamics classes.

If you think it might work for your purposes, here is a course by the program's creator from MIT's OpenCourseWare site. Lecture 3 is a tutorial on how to use XFoil. You might want to browse the OpenCourseWare site for more advanced uses of XFoil, too.

Good luck!